Yes, a coin that's mined by "Proof of Carbon Capture" would be amazing, but I can't imagine how it would work. Decentralization and neutrality is hard/impossible once you're trying to interface with the real world. How could you verify the carbon capture without a centralized authority?

I can imagine it would be possible in the far future with automation/robotics verifying the captured carbon in a neutral and decentralized way, but with current tech I can't see how it could work without being susceptible to being gamed. But maybe I'm just lacking imagination.