It's cheaper, but the costs are external costs (calculated for the next 100 years about 600 Euro per ton of emitted CO2).

They could be internalized by CO2 pricing, such as CO2 tax or certificates

Fossil fuels are cheaper because nature did the energy intensive "turn dinosaurs into oil" part (i.e creating the hydrocarbon molecules) for us over the span of millions of years and we just extract it from the ground and do some chemistry magic to make it into useful stuff.

The "create the useful hydrocarbon out of atmospheric carbon" step needs to necessarily be cheaper than getting dead dinosaurs to a refinery and refining them.

Screeching about externalities adds nothing to the discussion. Burning synthetic hydrocarbon fuel would also release carbon. A CO2 tax would hit it just as hard as it hits traditional hydrocarbon fuels unless you do stupid "craft the tax to pick and choose winners" crap that a carbon tax is explicitly supposed to avoid.

It wouldn't because as a producer you would remove CO2 from the atmosphere which brings its carbon footprint close to zero