Jumo 004 ran on kerosine.
From what I've read the synthetic fuels used by Germany became a problem in the additives which had to be used in them, and yes they were expensive to produce. On the positive side, when high octane (C2) was switched from natural manufacture to synthetic (C3) it was because it was actually no more expensive or difficult to produce than the standard grade synthetic avgas B4. But the problem here was through extensive testing it was decided that the amount and kind of additives in high octane synthetic fuel was problematic for aero engine maintenance and serviceabilty (I've read a German report on this).
Instead they decided to further develop combustion chambering and piston crown shapes in order to lower the knock rating of a given engine on lower grade fuels. The report is quite detailed about this, the RLM most definitely preferred the standard grade B4 fuel for high performance German fighters wherever possible right to the end of the war.
C3 was used, according to these RLM reports only out of sheer necessity for inline engines and inevitably development would continue until a new model could again use B4 at the same or similar performance standards.
This might translate to modern arguments about alternative fuel sources, that using them is a very expensive proposition, not just for manufacture of the fuel in the quantity required, but for actually using it exclusively among engineering standards which were developed using natural based petroleum fuels. You need to essentially reinvent 150yrs of combustion engine development. Doable in the computer age but expensive I'm sure to put into practise on a large scale.
