I don’t think this would be a good idea… these areas are not the result of desertification but are naturally desert ecosystems. The only way to make them anything else would be to take even more water from bordering non desert areas, which are already severely impacted by all of the water taken to support huge cities and green lawns in the southwest deserts.

For carbon storage it would make more sense to regrow forest in places that naturally have water and soil that support forest.