I agree. It's the sensible thing to do politically. But if US won't supply F-35, why would they allow KAAN to be supplied with a US engine?
For one simple reason: The Americans cannot stop the KAAN project.
In fact, I am very sure that they know exactly when the Turkish engine will be ready and what specifications it will have.
From the American point of view, a refusal by the US government to export F-110s would be useless and completely counterproductive.
Turkey would be doing several things at once.
1. end the joint venture with TEI and GE, dissolve TEI in its current form, at least in this form. The Americans would then be completely out of the Turkish defence industry as far as engines and other cooperations are concerned.
2) Turkey would knock on the door of Russia/China to get a suitable engine for the prototype and for the first blocks, and the Russians or Chinese would even be prepared to supply them, including a technology transfer.
Because they know very well that Turkey has a geopolitical and strategic value, and Turkey as a NATO member becomes even more uncontrollable.
It would only be a member on paper, because the relationship between NATO and Turkey is already very ambivalent and fragile, and the damage would be almost irreversible. Domestically, this would be the ammunition Erdogan needs to further unite the population and consolidate his position: "They don't want us, they don't accept us and they don't trust us.
It would even give him a massive political boost, because the national consciousness in Turkey ticks in a completely different way to anywhere else in the world. In contrast to Europe, the Americans know that you don't divide the country by attacking it too much politically and economically, but that all parties and citizens voluntarily or involuntarily pull together - even parties like the DEM would have to bow to this social pressure.
3) Turkey would even consider kicking a large part of the Americans out of Incirlik and other bases completely.
4) Turkey will then have no inhibitions about buying complete weapons systems from non-NATO countries, e.g. aircraft for the navy, where both the US and Turkey hope to somehow solve the F-35 <-> S-400 problem in a face-saving way for both sides.
So the Americans lose more than they gain by refusing. The indigenous engine will come either way, whether in 8, 10 or 12 years, it doesn't help them to destroy important relationships if they can't change anything.