Because it's too late. Unless magic non-existent carbon capture technology materializes soon, we're basically fucked.
https://www.vox.com/2016/10/4/13118594/2-degrees-no-more-fos...
Check out that middle graphic. If we really want to avoid 1.5 degrees, and we can’t rely on large-scale carbon sequestration, then the global community has to zero out its carbon emissions by 2026.
Ten years from now.
That article is two years old and, to state the obvious, global CO2 emissions are not on track to reach zero in the next eight years.
No we can't, because most of the CO2 has already been emitted: https://www.carbonbrief.org/analysis-four-years-left-one-poi...
Unless you invent a time machine, or as postulated by OP, some magic sequestration technology to pull CO2 out of the atmosphere and put it back in the ground, it's too late.
It's like we're in a car that's driven over a cliff, and you're saying "Well, we're still here, as long as we invent a way for this car to fly in the next 15 seconds before impact, then we'll be okay"
So the billion dollar reward would be quite small sum in the grand scheme of things. And for example with a carbon tax, where collectors could offset emitters, it might also become a quite lucrative business.
Unfortunately we haven't invented the technology to implement your broad brush "solution" either.
In fact, I'm skeptical about the claim Climate Change could have been solved generations ago, given that we still haven't developed the means to do it yet.
Edit: okay, perhaps nuclear could provide us with the masses of power generation we need, but that's been ruled out.
Path dependence. We have not developed the means to solve climate change from where we are now.