Asserting that there is a very bad solution which should be ignored doesn’t require me to write in detail about biological sequestration improvements, which I have published on at length.
These approaches have multiple value propositions, but mechanical carbon capture has only one that has scaled in any way, which is to provide a PR fig leaf for the fossil fuel industry.
Avoiding producing CO2 is much more cost and time efficient than any mechanical CCS solution.
As for nuclear, that it’s the most expensive form of new generation that can be built and isn’t getting cheaper can’t in any rational view make carbon capture cheaper. Expensive times expensive=expensive.
I would recommend you reconsider your sources of information and perspective on solutions.