The catch is that the diaeresis in Türkiye does something completely different that the diaeresis you mentioned, so actually it would be less confusing if English didn't have it at all.

...then again, even some Germans are using the diaeresis for this purpose, such as this guy https://en.m.wikipedia.org/wiki/Bernhard_Ho%C3%ABcker - and you can't blame him, because usually "oe" is a transliteration of "ö", and then his name would mean "hump" (as in camel's hump).