I think, in comparing the energy input and output of the fuel, you might be omitting its storage density and role in off-grid energy availability. For example, consider aviation: you can't hook up a plane to a solar farm or nuke plant, but you have to take energy with you onboard. In order to fly and lift passengers or cargo, you need to minimize the mass of energy supply, which means maximizing energy density. It's really hard to beat hydrocarbons for that, and they're available at a convenient range of temperatures and pressures. So, the idea behind synthetic fuels is to make artificial hydrocarbon fuel as a means of storing green energy. The energy input-output inefficiency is just the price of storing that energy for off-grid use.