CC sounds like plastic recycling. A pseudo-solution to maintain the status quo that will take decades for us to realize it does not work.
What might also happen is some sort of "risk compensation": the fossil fuel industry, politicians, and regulators will relax their stance against fossil fuel extraction because "CC takes the CO2 off the atmosphere" - like they did with plastics - and when we notice it, the net emission of CO2 per year will never decrease.
Those are real dangers.
Keep the oil in the ground.