[goodoldneon]

It isn’t for all repeated vowels; only for when the 2 vowels don’t make a single sound. So “chicken coop” wouldn’t have a dieresis

[stavros]

It would if the chickens formed a business structure that was owned and democratically controlled by its member-owners.

[goodoldneon]

Great point :D

[o0-0o]

That, is likely co-op.

[satvikpendem]

That's the joke.

[OJFord]

Unless it was a chicken coöp... One of few cases it actually resolves an ambiguity!

[Cthulhu_]

It's also to distinguish metal bands. Motörhead.