Noticing you skipped wind power there... Maybe because it doesn't fit in your narrative?

Also;

solar power - silicon is required - good quality, and we are running out of it fast

Rocks are made of silicon. It costs energy to turn rocks into solar panel suitable silicon, but not that much compared to a panel lifetime of turning carbon dioxide into carbohydrates. "We are running out" of the sources capitalism now considers suitable.

and also tons of metals required

Solar panels doped with non-rare metals (the sort you would have left over when turning rock into silicon) are only one or two decades behind rare earth solar panels in terms of yield. They aren't a priority in the current market, but that's because of extractivist capitalism rather than the laws of physics.

(and also battery materials)

You don't need batteries for carbon capture, you can just do it with the power that's in excess. In fact, if you're deciding to use solar panels for carbon capture, you need to massively overproduce solar panels relative to consumption, meaning you need fewer batteries than if you're not able to use excess solar power (because the solar panels powering carbon capture during midday can be used to power homes shortly before sunset).

geo/hydro thermal - not available evrrywhere

Completely irrelevant for carbon capture.

nuclear - one of the only sources which is realtively very clean

I also like nuclear, but now it's clear you're just being biased. Nuclear power plants require tons of rare materials built precisely or else disaster happens. Practically, they're less clean than wind, water, geothermal, and the (for now inefficient) rare earth free solar panels.

Also, there actually isn't enough projected-to-be-accessible uranium ore in the world to do more than 1% of the energy production necessary for carbon capture. We could try filtering it out of sea water, but that's more difficult and ecologically disruptive than turning rock into solar panel substrate.

can be even retrofitted to some large coal plants

Not really relevant for carbon capture, because we need to increase electrical production by a factor of 10 but retrofitting coal plants means you're reducing production instead. A nice way to reuse infrastructure, maybe, but even there it reeks of political wrangling.