This brings up something that is perhaps easy to forget: the interpretation of diacritics is far from universal. The diacritic in the character 'ä' can be one of two semantically different diacritics. It can be a diaeresis, a diacritic whose function is to mark that vowel starts the next syllable rather than existing as part of a diphthong; or it can be an umlaut, whose purpose is to indicate that it is a different vowel sound altogether. As far as any charset is concerned, though, despite those very different semantics, the two things are the same diacritical mark [1].
Even beyond the issue with two concepts using the same glyph, the interpretation of the same diactrics among different languages is inconsistent. English tends to drop diacritics to the point that many people think that English doesn't use them; German uses expansion (so ä becomes ae). As you mention, some languages are incomprehensible either way, so they need to be preserved. And sorting and collation is even more fun!
[1] This does mean that Unicode's insistence that characters represent semantic differences rather than graphical differences can come across as rather arbitrary. The original purpose of Unicode was to unify different character sets together, so it preserves character differentiation that existed in antecedent charsets but tends to otherwise unify characters in practice.