Spending energy that likely came from fossil fuel burning to "capture" CO2 is like saying you've found a perpetual motion machine. The engineering is simpler for this in some ways, but it's still not really a "good" solution.
I agree organic capture is a good idea, and CHEAPEST thing we could do to have an impact dump iron into the open ocean to spawn a phytoplankton bloom, but there is no money to be made doing that.