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).