Nuclear is very clean. What most people came to hate is the waste, which is surprisingly little (per kW). Also the danger in case of failure, which is massive.
We have no practical way to clean CO2 from the atmosphere and we don't need catastrophe for it to be a problem. We're poisoning the planet with real carbon dioxide while we fret about the hypothetical risks of hypothetical nuclear waste.
We could replace coal with nuclear yesterday if the anti-nuclear activists would stand down. Instead, they have fought to continue a status quo whose death toll we start couting at 25,000 people per year lost to black lung [0]. No serial killer or terrorist could dream of effecting mass casualites as efficiently as the proponents of this viewpoint do when they take action that results in the continued and expanding operation of coal power generation, despite an alternative which is actually viable in every respect but their opposition.
Yes, nuclear power has problems. But even if it killed 24,000 people per year, blocking the replacement of coal by nuclear would still be a willful choice to cause the deaths of 1,000 people (it's getting really hard not to say murder).
The total volume of which would fit in an apartment block. That block could be dropped into the marina trench if you really are that paranoid, total cost a few million dollars.
There is no conceivable way of removing even daily worldwide human carbon waste from the atmosphere for that kind of money.
Theoretically, we can put CO2 back in the bottle. Practically, we can do it now, just not with enough efficiency and scale to make it worth it.