I think, what’s the point? You know how cooperate is pronounced. You know that being naive is not being a knave.
Not everybody does know that, especially not non-native speakers, which English obviously has in abundance.
Dieresis is not really the best symbol for this given that it's much more commonly used for completely different things in other languages, but at the very least it makes you stop and consider why it's there in an unfamiliar word, and perhaps check its pronunciation in a dictionary.
(The more sensible thing would be to use the apostrophe as syllable separator where necessary, as in na'ive, co'operation etc - it is already frequently used this way in English in foreign names anyway, and is much more intuitive for non-native speakers.)
I'm not a fan of dieresis for this specifically because it's too confusing due to its frequent use for other things in other languages. But there are other ways to indicate it.
Comments
Not everybody does know that, especially not non-native speakers, which English obviously has in abundance.
Dieresis is not really the best symbol for this given that it's much more commonly used for completely different things in other languages, but at the very least it makes you stop and consider why it's there in an unfamiliar word, and perhaps check its pronunciation in a dictionary.
(The more sensible thing would be to use the apostrophe as syllable separator where necessary, as in na'ive, co'operation etc - it is already frequently used this way in English in foreign names anyway, and is much more intuitive for non-native speakers.)
As a non-native speaker, coöperate does NOT help, it makes it harder to recognizes otherwise familiar words.
Especially when one comes from a language where ö is a completely different letter than o.
I'm not a fan of dieresis for this specifically because it's too confusing due to its frequent use for other things in other languages. But there are other ways to indicate it.