Clever, but stupid. Sucking CO2 out of the air requires energy. Less energy with this idea, but energy nevertheless. That energy is generated with something that contributes to the level of CO2.
If you suck CO2 out of the air, plant life will grow less lavishly to compensate for the reduced CO2, and that will reduce the amount of oxygen in the air which will impact animal life which will produce less CO2. Get where this is going? Nature is self-correcting.
Yes, let’s bring on the ice age.