A possible reason is that the engines of the new LW aircraft demanded synthetic oil and were unfit for high octane fuel .
We may be having a translation problem here.
You can almost always use higher octane fuel than an engine
requires. With leaded fuel that can lead to lead fouling of the spark plugs but for short range fighters that means 5-10 flights before the plugs even need to be pulled for inspection.
There was no special property that synthetic
feed stock (the stuff you start turning into finished product) has over natural feed stock (crude oil).
You seem to fishing for reasons.
Allied and German fuel varied enormously in the amount of aromatic compounds.
The Americans started with 2% or under for 100 octane fuel.
The British started with not less than 20% for 100 octane.
The Germans at times used up to 40% for 96 octane.
ALL aviation fuel was blends of different compounds and additives. There were hundreds of possible combinations that could get to the pretty much the same end result.
The Germans tended to use high cylinder compression for better economy in the V-12s while the allies used higher boost.
The Germans tended not run their engines as rich as the allies did at max power. This affects both economy and cooling. P-47s were famous for leaving black smoke trails on take off they were running so rich as they were using some of the excess fuel as coolant.
This is a complicated subject that has few good commonly available sources.
The Germans would have loved to use higher octane fuel, the problem was making it with resources they had available. As an example toluene is a good additive to gasoline to raise the octane rating. You can get toluene from natural crude, you can also synthesize it. Unfortunately it is also a prime ingredient in TNT. Germans invented TNT (?) so they new about it and how to make it. Question is can they make enough or do they need to use something else in the Av gas or do they use us a little toluene and then something else?
The whole supply thing is very complicated and cannot be reduced to a few sentences and/or paragraphs.