But then, you have to distill it and strip out the sulfur and other elemental contaminants and fractionate it and crack it... one benefit of starting off with pure CO2 and water is the ability to selectively make pure hydrocarbon fractions (or at least fairly restricted spreads of chain lengths) without having any waste.

Also, there's the distribution issue - this could all be done regionally, so transport costs will go way down. The only thing needed is excess energy to dump into the process (equatorial zones would be good for solar PV inputs, etc.)