>SO if you have free energy about to do carbon capture you are MUCH better off just using that energy to do what ever you were burning the carbon for in the first place!

There are a variety of applications where being tethered to a grid or using a battery are not practical. Fuel is convenient because it has insane energy density and certain kinds of fuel can be kept for years without degrading. The amount of raw energy contained in a sizeable gas can would be too heavy for a human to carry if it were a battery. A $20 gas can with $4 of gas contains more energy than my $25,000 battery backup system, for example. And while extracting useful work from fuel is often inefficient, using the fuel for something like heating is practically 100% efficient.

Long story short, we will always have a use for fuel, so being able to sustainably produce it is useful.