I'd personally much rather see the source of the problem fixed (reduce carbon emissions). I also hope this doesn't turn into an excuse to clear-cut more rain forests.
i.e. We'll cut down the real trees and replace them with efficient carbon collecting "tree" buildings.
This is a very poor substitute for trees. Trees convert gaseous carbon dioxide into solid organic molecules [1].
I am pretty suspicious of the idea that humans (especially the humans who come up with the lowest bids to win these contracts) can store planetary-scale amounts of carbon dioxide over geologic time.
It would be very interesting if one of these technologies eventually made carbon capture so cheap that multiple countries could single-handedly afford to reduce carbon levels to whatever they wanted.
At that point carbon levels become an active decision. The words environmental policy would take on a completely different meaning.