The problem is purely thermodynamic. Plants transform co2 in useful compounds that do not contribute to greenhouse effect.

Any capture system is a temporary storage of co2 that has anyway to be transformed, because co2 is loosely trapped. Scientifically is literally sweeping dirt under the rug. There is no long term benefit (as at some point in the future you'll have too transform more co2 than what in the atmosphere), it costs a lot, and gives a fake sense of "trying to solve the problem", while it's doing nothing