A nice explanation for the sodic nature of Archaean granitoids was suggested by Oliver Jagoutz at the Goldschmidt Conference last year:

http://goldschmidt.info/2013/abstracts/finalPDFs/1374.pdf

As for the lack of S-type granitoids, that is likely related to the general scarcity of sediments in the Archaean. This would be consistent with a hotter lower crust at the time and thus difficulty with supporting large orogens and hense less weathering:

Flament, N., Coltice, N., Rey, P.F., 2008. A case for late-Archaean continental emer-gence from thermal evolution models and hypsometry. Earth Planet. Sci. Lett.275, 326–336.

Flament, N., Rey, P.F., Coltice, N., Dromart, G., Olivier, N., 2011. Lower crustal flowkept Archean continental flood basalts at sea level. Geology 39, 1159–1162.

Less continental free-board would be even more pronounced if the ocean volume was indeed greater back then as suggested in this paper:

Pope, E.C., Bird, D.K., Rosing, M.T., 2012. Isotope composition and volume of Earth’searly oceans. Proc. Natl. Acad. Sci. U. S. A. 109 (4371), 1–6.

Thanks, Kristoffer! Your answer is useful. 

The lack of sediments in the Archaean is a condition, and another possibility may be because that the scare and short-lived sediments cannot be subducted into the deeper earth. Since the  melting and differentiation are involved in high temperature and certain pressure, so a subduction process is a requisite condition. And the tectonic enviroment to form the S-type granites are usually related with the subduction environments. 

Thanks, Meng Jie. If sediments could not be subducted, where they have gone? Why were they short-lived? Many workers believe that at least some form of subduction was prevalent in the Neoarchaean. Any alternative idea from others.

So this is a problem leading to two opposite views. I think another tectonic model different from the subduction model existed in Archean. Many factors were largely different from that at present in Archean. So sometimes we cannot compare the Archean rocks with the newer rocks. In that time, the crust might not be present,and actually the high temperature on the earth surface and the high geothermal gradient  made the sediment  short-lived. Though detrital zircon told us 4.0Ga existed, the old rocks didn't be founded. So I think some form of subduction different from the general subduction process possibly existed, so more evidences are needed to confirm wherther subduction exsited in that time.

I also think that some form of recycling of continental crust, different from that of present day, existed in the Archaean.

If you have no thick continental crust, you'll have no large sedimentary basins (e.g., passive margins), no continental collision and no S-type granites. 

Meng, continental crust had lower thickness, but oceanic crust could probably got very thick in Archean times (with large plateau with 30km thick, ?), then some crustal derived TTGs with lower MgO, Mg#, Ni & Cr did probably generated from partial melting of  the lower plateau oceanic crust. (see high-silica adakites)

My first idea when I saw the (very interesting) question was also 'not enough sediments', but then I am sitting here in South Africa on the sediments from the Witwatersrand and Pongola Supergroups. Next thought was 'not correct composition for sediments to melt', but some of them are actually nicely feldspathic, and therefore suitable for melting. Another thing to perhaps keep in mind is that we're talking about relative scarcity, so if there are a lot of other types of granites, then the "S-types" do not stand out any more. Perhaps we should also think of how we recognise S-type granites - typically by their peraluminous composition. But the composition of sediments is supposed to have been different in the Archaean and post-Archaean times, so that could also be a factor.

Prof Elburg has given a very thought-provoking possibility. In India, for example in Singbhum craton we have voluminous Palaeoarchaean metapelites. Melting of these metapelites would have produced typical S-type granites This craton have signatures of crustal recycling around 2.8 Ga producing granites without S-type signatures. Also in the Neoarchaean most of the cratons underwent extensive crustal reworking  which have produced only I-type K-rich granites. Then why the sediments present in the contemporary greenstone belts did not melt and produced S-type granites. I think we can recognize S-type granite with some confidence e.g presence of older zircon, zircon O isotope record, presence of metasedimentary enclaves etc. besides being peraluminous. Is this a matter of preservation that the S-type granite were mostly emplaced in the very upper part of the crust and a majority of them are not preserved at the present level of exposure due to erosion? 

If it is the RELATIVE scarcity, then we can of course also turn the argument around: why so many tonalites and metaluminous granitoids? They typically form at higher temperatures than S-type granites, and there are good arguments to assume that temperatures were higher in the Archaean earth than under present-day circumstances. Here in SA it doesn't seem to be a matter of the upper crust not being preserved - low-grade Archaean sedimentary rocks and greenstones aplenty.

I agree with colleague  of U.J, They typically form at higher temperatures than S-type granites, and there are good arguments to assume that temperatures were higher in the Archaean earth than under present-day circumstances. For more information you can read S-type granites and I-type granite per differences between their etc. 

As has been mentioned above, I would convene that the reason is the scarcity of sediment/sedimentation, but also I would add very rapid erosion rates among other factors. Indeed there are lots of evidence of basins and volcanoclastic sedimentation during the Archean, but fast rates of erosion would wipe them out quickly, counting the intense plutonism at that time and during the Proteroz. Someone above asked then where did these sediments go...to the continental platforms and further, if they did not get stuck in a basin. A nice example is the area of Elliot Lake, Ontario. There, you can see everything youmay have been asked about your question:

Archean volcanic activty and consequent sedimentation. Plutonism, diking, and fast erosion rates of intrusions, volcanic depositions and sediments, including the combo of glaciation cycles. To top it up, burial times of sediments and later inversion in a northern prism of accretion was really fast. A similar very fast sedimentation and burial of sediments can be found in the English River basins, near Red Lake area in Ontario.

However, the problem remains unresolved. In many cratons we get Archaean sediments aplenty, which do not bear evidence of fast exhumation after burying so as to escape melting. As Marlina said earlier, many of the Archaean sediments have ideal compositions to form typical S-type granites. Given the common occurrence of Archaean pelitic granulites (indicating deep burial) and higher geothermal gradient, it is still baffling why production of S-type granites were not common. Otherwise, is it a matter of preservation? 

Some Archean cratons, such as the Superior Province of Ontario, Manitoba and Quebec, have abundant S-type granites mostly associated with high grade metasedimentary belts:

 English River terrane (e.g., Wapesi Lake, Churchill Lake and Allison Lake batholiths), Quetico terrane (e.g., Glacier Lake batholith) and Opinaca terrane of Quebec

 domain boundary zones such as the Sioux Lookout terrane (e.g., Ghost Lake batholith) and major deformation zones in North Caribou terrane (e.g., Pakeagama Lake pluton in Favourable Lake fault zone)

I spent much time on reconnaissance mapping projects in NW Ontario that covered about 140,000 km2 of the Superior Province. Within the English River terrane approx 5000 km2 of peraluminous, S-type granite (diatexite) were delineated within the western half of this 1200 km long metasedimentary belt.

Slide # 14 in link below that shows the general distribution of the largest S-type granite masses in this terrane.

https://www.researchgate.net/publication/266203573_Fertile_peraluminous_granites_and_related_rare-element_pegmatites_Superior_Province_of_Ontario_Powerpoint_Presentation

A review paper on the English River subprovince:

https://www.researchgate.net/publication/268448987_English_River_Subprovince_review_paper

The most detailed documentation in Ontario of a peraluminous, S-type granite complex involves the Ghost Lake batholith that has an interesting association of rare-element (Li-Rb-Cs-Ta-Be) mineralization:

https://www.researchgate.net/publication/266318924_The_Ghost_Lake_batholith_Superior_Province_of_Ontario_a_fertile_S-type_peraluminous_granite-rare-element_pegmatite_system

A recommended review paper on general geology and metallogeny of the Superior Province can be found in Percival (2007). A revised terrane subdivision map of the Superior Province in Ontario was published by (Stott 2011).

http://www.geologyontario.mndm.gov.on.ca/mndmaccess/mndm_dir.asp?type=pub&id=MRD278

Hope this info helps.

References

Breaks, F.W. 1991 The English River Subprovince, p. 239-277 in Geology of Ontario, Ontario Geological Survey, Special Volume 4, Part 1, 711p.

Breaks, F.W. and Moore, J.M., Jr. 1992. The Ghost Lake batholith, Superior Province of northwestern Ontario: A fertile, S-type peraluminous granite-rare-element pegmatite system. The Canadian Mineralogist, v.30, 835-875.

Breaks, F.W., Selway, J.B. and Tindle, A.G. 2006. Fertile and peraluminous granites and related rare-element mineralization in pegmatites, north-central and northeastern Superior Province. Ontario Geological Survey, Open File Report 6195.

Breaks, F.W., Selway, J.B. and Tindle, A.G. 2008. The Georgia Lake rare-element pegmatite field and related S-Type, peraluminous granites, Quetico Subprovince, north-central Ontario. Ontario Geological Survey, Open File Report 6199.

Percival, J. A. 2007. Geology and metallogeny of the Superior Province, Canada, in Goodfellow. W.D., ed., Mineral Deposits of Canada: A Synthesis of Major Deposit-Types, District Metallogeny, the Evolution of Geological Provinces and Exploration Methods: Geological Association of Canada, Mineral Deposits Division, Special Publication No.5, 903-928.

Stott, G. 2011. A revised terrane subdivision of the Superior Province in Ontario. Ontario Geological Survey Miscellaneous Data Release 278 (see zip file).

Conference Paper Fertile peraluminous granites and related rare-element pegma...

Chapter English River Subprovince [review paper]

Because  S type Granites  normally  associated with Archeaen Metasediments 

Dear Sukanta Dey,

The current explanation of granitic rocks formation is not well made is over simplified (That is why you reject positive answer to the next questions: “Why? Is it related to the lower crustal thickness in the Archaean so that sediments could not be buried to deep levels and get melted? If the continental crust had lower thickness, then why some crustal derived TTGs (lower MgO, Mg#, Ni & Cr) display high-pressure signatures? “… I think the granitic rocks research needs near the analyse of granitic minerals (chemical compositions)… Relation of granite bodies with their environments (their contact with the neighbour sediments, geophysical  effect,… )… their role in region volcano activities, metal-genetics… Their contains of rare earth elements (REE)…

So needs rethink the formation of granitic rocks their genetic separation (metamorphic, plutonic)… These two types are strongly different, their origins need some rethink… (my opinion first arisen when in Hungary was found oil in metamorphic rocks and their explanations was very hard… another good example is relation to your subject…   SYENITE FROM THE DITRĂU

http://www.mindat.org/loc-214594.html

http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=1114&context=geologia

Dear Frederick Breaks, your observation – if I have understood well – contradict my previously made comment…

But something important interesting things are REE to the mentioned S-type granites!…. Your examples are from such a zone, where can find good explanations, answers to Dey questions… And test the current Theory of granite formation tip batholitic (plutonic)… IF the presented S-type granite are batholitic, they has connection with REE… Has strong thermic contact with the meta-sediment or other rocks indifferent of their type… If mentioned characters cannot be found, we have meta-sediment formed from S-type granite… The S-type granite presented by Frederick, is not comes from the melted sedimentary rocks…    

P.S: These assumptions was made without have any knowledge of granite shown by Frederick…

Dear Laszlo-Attila,

Thanks for your response.