Carbon capture (more specifically direct air capture) is not a viable option due to the energy requirements and the low concentration of CO2 in the atmosphere. Carbon capture is largely promoted by fossil fuel companies for the same reason that recycling is: “let us keep doing what we’re doing because there’s some magical way to undo the damage, we just need a few more years of research”.
However, plants do the same thing and already exist. Trees in particular have shown some promise for being able to be a precursor for many polymers. This would at least mean that any plant matter used for this did pull CO2 out of the atmosphere in the last few years (so relatively neutral compared to the other options), whereas fossil fuels are releasing carbon that was removed from the atmosphere millions of years ago.
EDIT: TLDR, oil drilling should be banned or severely limited, but DAC is not a viable option and is only relevant because oil companies keep pumping money into it. Biomass is potentially an ok feedstock for plastics (but not for fuel).
The problem with using wind and solar is that you’d need a lot of it due to the energy requirements. While both should be used extensively, there comes a point where the resources required (these would likely use precious metal catalysts) to build the CCS plants and all the power infrastructure for it and waste produced makes it the obvious choice to just use trees.
If you look at how trees function, it is an incredibly complex process with some rather extreme conditions which are difficult to replicate with machines. If someone does manage to get it done efficiently then that’s great (though I think this is unlikely). But I don’t want it to become like recycling did: an excuse for companies to do whatever they want. The original expression was “reduce, reuse, recycle” with recycling being the last resort, but now we never hear about the first two because they get in the way of obscene profit.