Rules for thee, but not for me.

coöperate – we used to have a diaeresis on the second ‘o’ to indicate a second syllable (and to make it clear we weren’t talking about barrel making) but then we decided we hated accent marks …

Typesetters decided we hate accent marks
- The New Yorker would like to have a word.
- Typesetters were right.
As a German, it's a welcome change.
Imagine your head automatically pronouncing the "ö" of coöperate like this:
https://en.m.wikipedia.org/wiki/Close-mid_front_rounded_vowel
- the pain of being nordic/german, you're utterly incapable of taking anglophone metal albums seriously
  "motörhead", yeah sure, mote 'er head
bring back accent marks!!

Isn't that right in the definition of the word? They co-operate to form a word.

Cooperating means working together to accomplish a goal, sometimes by doing different tasks; not necessarily just doing the same thing and duplicating effort, as would be the case if they made the same sound.

If anything, we should be casting shade at that lazy hyphen who ducked out early instead of sticking around to make the etymology clear.

Cooperating, to make a barrel.
- That one took me a moment... 😁

As a native english speaker, english is stupid.

All languages are stupid. Japanese has 3 different scripts, with the kanji having made up characters that don't even mean anything. Chinese has a coherent grammatically poem where every word is just shi making "Buffalo buffalo buffalo Buffalo buffalo" look like child's play. Romance languages felt it necessary to give every noun a gender that you have to memorize, and German decided that wasn't complicated enough so they added a third gender. Welsh and Gaelic use the latin alphabet, but just made up their own rules so the language doesn't sound anything at all the way it looks to other languages that use the Latin alphabet.
All languages are messy and illogical since they evolve over time to accommodate the needs of the speakers at any given time, and then you end up with weird holdovers that no longer make sense, but that's just how things are done so we keep doing it that way. Artificial languages have been created to maintain a logic, but no one uses them, and if they were adopted universally they would lose that logic as people use the languages in ways that were never intended.
- It's the whole reason science stuff tends to use latin as much as possible. It's a dead language that is relatively easy to learn, but won't evolve over time as no one is casually using it.
- Hey, the three Japanese script make actual sense though.
As a native Slavic language speaker, wanna trade your tense system for our noun cases?
- My native has 19 cases with 2-3 variations of each for vowel harmony. Plus verbs are partially conjugated for both the subject and the object, so I see you, you see me, they see it are all one word sentences each, just conjugated differently. I see myself is a two word sentence though, with both words conjugated.Other simple sentences are also collapsed into conjugation hell, "You could take me home" is one such heavily conjugated word.
  But no genders, and only two and a half temporal tenses, and pronunciation is directly matched to text, no pronunciation guides or spelling bees.
As an attentive English student, I must disagree.

And yet they exist side by side in the same word. Pretty much the definition

Doesn't prevent them from working together.

Unity in Diversity

Historically you would use the umlaut (lit. re-sound in German) to signify that both vowels are pronounced separately and not as a diphthong! I think some publications, like The New Yorker, are pretentious enough to still use it.. In this case, cooperate would be spelled coöperate.