> It’s fine to emit a small amount of co2 to extract a larger amount.
No it is not.
Simple example: if you need 1000 times the remaining fossil fuel on Earth to extract the CO2 needed to "save the climate", then by definition you simply don't have remotely enough energy on Earth to do it, so your system is not only not viable, but it's counter-productive because it is using some of that remaining fossil fuel for almost nothing.
