> it doesn't make sense to use some of that energy to remove some of that CO2.
Of course it does, if the price of CO2 is high enough. If I can capture 1.1 unit of CO2 per unit of CO2 released and it still makes me money, I'll use any energy available. This could happen if e.g. the government subsidizes carbon capture credits or simply if an efficient enough process exists.
On top of that, if the price is high enough it would be viable to build renewable energy solely for powering carbon capture.