One shortage is for example the high amount of residues remaining on the soil surface resulting in difficulties in seedbed preparation and successfull germination.

As a researcher from the developing world, I can tell you that the economic barriers to the adoption of no tillage agriculture i.e. buying equipment is a major constraint. So technical issues arent the only ones to consider.

Not only the equipment but the non-availability of effective post emergence herbicides as well as herbicide tolerant crops are one of the hurdles for conservation agriculture. Moreover, the low cost equipment for CA are being started manufacturing in India by local manufacturers in Punjab state.

No tillage can not be directly related to carbon sequestration, often it relates to redistribution of carbon stocks in soil profile like discussed in "Tillage and soil carbon sequestration—What do we really know?".

The results from our long-term experimental site close to Vilnius (LT) showed no subtantial changes in SOC after cropland convertion to no-till practices. In addition CO2 measurements in central Lithuanian did not find reduction in CO2 emissions related to reduced tillage.

Dynamics of SOC seams to be different, depending on soil and climate conditions?

/see: Giacomo DeSanctis et all "Long-term no tillage increased soil organic carbon content of rain-fed cereal systems in a Mediterranean area"

as far as I understood they also found  redistribution of SOC "was significantly higher in the top 10 cm of the soil under NT than CT, but it was similar in the 10–40 cm layer", while conclusions on significant SOC increase been based on DSSAT simulations.