It is understood that high surface area carbons (>1500 m2 /g ) store Li+ at the surface through many mechanisms and resulting capacity is in the range of 1500 mA h /g . This value is much greater than graphite (350). Then why these materials are not used / no significant research in last 5 years..
Without knowing the specifics of your question (what carbons exactly?), the presence of redox active functional groups on the high surface area carbons may be an issue. Additionally, electrical conductivity or just chemical stability may be an issue with the high surface area carbons. Finally, as your question really is why the high surface area carbons are not being studied, it is always possible that people in the field feel graphite has more potential, either due to the issues I mentioned, or because the high surface area carbons seem to have reached a limit.
Compare the volumetric capacity! ;)
But there are also other issues like price, side reactions with electrolyte, processing problems during manufacturing and so on...
High surface carbon means much contact area with the electrolyte, leading to an increased formation of solid electrolyte interface (SEI) on the carbon surface. This formation consumpts Li-ions irreversibly which are assembled in the SEI layer as inorganic lithium compounds like Li oxides, -carbonates etc. which cannot be reused for charge/discharge of the cell. For this reason, a high surface carbon (or other active material) shows a very high inital capacity loss.
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