Many climate control projects have hard-to-judge side effects and are currently either hard/expensive or impossible. It is cheaper to not burn the carbon in the first place. Carbon capture might be easier to control as a single entity (a definite benefit), but there is no money in it as of now, so research is slow.

On the other hand, all current IPCC scenarios require both lifestyle changes and a staggering amount of carbon capture, starting from 2030 peaking with up to 20 Gt/CO2/year in 2050 for the worst scenario (which we are very much on track for) [0]. (Current emissions are around 40 Gt/CO2/year. [1])

Nobody knows how, and especially not how without side effects. That does not mean we should not try - we need to - but that means we have to pull all the stops, now.

Look at those plots, this is a desperate situation, and the IPCC reports are actually optimistic. [2]/[3]

[0] https://www.ipcc.ch/site/assets/uploads/sites/2/2019/02/SPM3...

[1] https://www.ipcc.ch/site/assets/uploads/sites/2/2019/02/SPM1...

[2] https://www.ipcc.ch/site/assets/uploads/2018/02/FigSPM-10.jp...

[3] https://www.ipcc.ch/sr15/graphics/