It is possible, it’s just expensive.

The U.S. navy is interested in a fuel synthesizer that works on co2, seawater and uranium and they can pay more than you per gallon because you don’t have to refuel an aircraft carrier in a war zone.

I fully agree with the bit about atmospheric carbon capture. What a pointless waste of energy. But if you start thinking of plant biomass not as the energy source, but just as the carbon provider for making carbohydrates from your hydrogen, then energy crops vs food crops conflict suddenly disappears, because the nutritious parts usually come alongside plenty of lower energy "plant waste" that should be good enough as a carbon provider for hydrogen "carbonation". Certainly much better for the task than atmospheric CO2. And all that plant carbon would soon continue it's cycle as atmospheric CO2 anyways, so it's just as good as atmospheric capture.