It's still sponges, not patches. They absorb the water, and you have to manage them. If you don't actively store them, the water will leak out. If you do actively store them and then hand off storage to someone else, the water will leak out when that someone stops paying attention.

The way to sequester carbon with trees is to cut them down when they're grown, and bury them somewhere where there's no air and no one will touch them for thousands of years, or otherwise store them in perpetuity while preventing decay or burning.