Hmm, maybe because they could, after all they’re german engineers
But depending on how the situation developed I would rather think, that going faster and higher is a pretty much obvious choice for aircraft developers. They would get the money if their US collegues get the money, cause if one side feels threatened it’s usually a mutual feeling, meaning if the US thinks of ways to deal with germany so would germany both offensively and defensively.
p.s.
The TA was service ready in 1945, I think there was still room for improvements till 1947, but yes the opportunity window wouldn’t be all to big. But then till 47 we have a pretty sophisticated radar network imho and maybe we have somethink really stylish by then, such as the Horthen IX.
Oh and I meant the max altitude, sorry for the confusion.