[a4isms]

I worked for GitHub for a time. There was a cultural abhorrence of the diaeresis, it was considered reader-hostile and elitist. I refused to coöperate with that edict internally, although I grant that every company has the right to micro-manage communications with the public.

[relaxing]

It is reader hostile and elitist.

Is there any good argument in favor of it, or any other house style quirks for that matter, other than in-group signaling?

[randusername]

It exists to indicate how a word is pronounced. Naïve is a better example IMO, cooperation feels too familiar.

Non-native speakers might see something like "nave" instead of "nigh-eve" unless it is clear that there is a stress that breaks out of the diphthong.

I don't think style guides are (usually) about absolute correctness, but relative correctness. A question is asked, a decision needs making, someone makes it, and now a team of individuals can speak with a consistent voice because there's a guideline to minimize variation.

[akramachamarei]

IIRC it's use is to distinguish vowels that belong to separate syllables with vowels which form a diphthong. I think this could be beneficial to language learners, to give them a hint that cooperate is pronounced "ko ah puh rayt" instead of "ku puh rayt", and likewise naïve as "nah eev" than "nayv" or "nighv".

[hluska]

You’re replying to a troll - their entire argument was circular and self contradictory.