Only problem with that is the Nazis did give their allies a lot of equipment, the reason they weren't giving more was lack of material for their own military.
US units weren't ever in that sort of situation ... If you've got all that extra stuff and lack enough manpower to use it, it makes a lot of sense give it to allies to use. The Germans had the opposite issue: too little stuff and too many men needing it across multiple armies. That problem only got worse from 1941 as there was mass losses of equipment in the field for European Axis armies (think Italians in Operation Compass and the Germany military itself in the winter campaign in the East). Even though production increased, it never kept up with the growth of Axis armies and losses. Despite that the Germans still equipped Hungary, Romania, Italy to a degree, and various other armies with German equipment or captured French equipment, while they themselves were having to use captured equipment in 2nd and even front line roles.
the case of Hungary and Romania is interesting, their blood feud was never settled only deferred. Germany encouraged the buildup of Romanian forces for prospective invasion of USSR but by 1944 it turned around like Frankenstein's monster and attacked them, ending the war earlier.
they would have been far better position (of course with hindsight) giving all territory up to Carpathian Mtns. to Hungary and collaborating with them to develop a decently large Hungarian air force. hand over production of HS-123 would benefit both. they delayed delivery of HE-112 again over Romania (mainly) https://en.wikipedia.org/wiki/Heinkel_He_112#Hungary otherwise the 123 & 112 might have been good groundwork for developing their air force. my understanding there were large number of JU-86 airframes that could also have been sent to Hungary for assembly?
(leaving aside whether they could further develop their turboprop design, which seems a good idea)