There is an important difference between AI risk and climate risk. The climate risk is indifferent to humans. This isn't ideal. But AI risk might deliberately try to bypass or thwart or adversarially remove human agency, which would be bad in a different way.
Climate change, or specifically rising CO2, something that is undesirable and requires technological fixes, has been hijacked by disaffected socialists in the wake of the fall of communism as a political excuse to try and tell people how to live. They've taken a tractable problem and turned it into a political battle and power grab. Let's not try repeating that somewhere else. Incidentally, that's exactly what the "AI doomers" are already doing, trying the political angle to gain advantage and power for themselves.
Carbon capture is not going to get us out of this.
If you have a problem that is caused mainly by over-consumption but your approach is to just wait for a sort of tech-hail mary to come; it's a logically flawed approach. It seems more reasonable to me to stop the cycle of consumption, then focus on making our industries "green" and increment consumption insofar the levels are within the margins of what we deem acceptable.
I mean, think of how we treat obesity, you don't just send people to surgery right away (and good thing there is surgery at all) it's a lifestyle change.
Now. I think most governments actually kind of take the approach you propose, and so I totally agree with you that please no; let's not do that because it's obviously not working for curbing climate change.
In the french citizen's convention for the climate there were several measures proposed for France to reach its 1.5C goal. Although I have some criticism to the practical implementation of the convention (not at all with the fundamental idea, which I think is definitely the way forward) it reached very interesting results. Now, it's not "the socialists" that hijacked the implementation of these proposals but the corporations through lobbying and conservative politicians that completely neutered the proposal. This is what's happening in reality, friend, not whatever fantasy you have in your head about a red scare.