Germany [0], as well as Apartheid South Africa (SASOL), and now China, synthesized that fuel from coal. Which is itself a fossil fuel.
[0] https://warhistory.org/@msw/article/synthetic-production-of-...
> Obviously, this will not be done as long as cheaper fossil hydrocarbons are offered. However the use of fossil hydrocarbons for plastic, asphalt or other applications that do not release CO2 is not harmful.
The issue with any fuel/feedstock production is not just the financial cost but the amount of energy returned on the energy invested. A modern civilization (like Japan) requires 10:1. Synfuels made using the method you described are 1:1 - they provide as much energy as it takes to make them.