I know that this was tongue-in-cheek, but I could imagine living in a world where naming countries as they name themselves is the dominant linguistic convention. Why not call Japan Nippon in a sentence.
You're free to call Japan Nippon as long as you're fine with people raising eyebrows, sometimes not understanding what you mean, or deciding you're a pretentious twit.
The request that we use a character that doesn't even exist in the English alphabet (ü) is particularly ludicrous.
It would make even more sense, after all we lose letters because we write those sounds using other letters or letter combinations, however the "ü" in "Türkiye" doesn't have an analogue in the existing alphabet.