Carbon capture will be a solution, it is just not there yet.

The problem is investment, if you decided to throw half of the money at CC that was thrown at the COVID response, so roughly a trillion dollars....CC would get there much faster. The best way to do this would be to tax the externallities of greenhouse gas pollution.

There doesn't seem to be any energy paradox with CC. Much like 400+% efficiency is possible with a heat pump by simply moving heat around rather than trying to create it directly, CC will have a ah-ha moment and we will get much higher kg of carbon / kWh than now.

My money would not be on a chemical process (better catalyst) but on a novel meta-surface that preferentially binds to CO2 in a reversible manner. e.g. the surface would be exposed to low concentration CO2 (air or sea water) and "charge up" with CO2 over a few hours, an electrical current would then release highly concentrated CO2 into a carrier fluid (air or water) which could be captured and stored in one of the many ways that have been proposed.
Most of the storage methods that have been proposed have been contingent on getting a concentrated source of CO2.