I would say that my answer about when to italicize loaned words and phrases is also the most appropriate answer to this question:
I think this is a case where authors can decide for themselves where to draw the line. Or, if the writing is for a certain publication, the editors will have a policy for whether a given word should or should not [have diacritics].
(However, that answer got zero votes, so who knows? I still think it is a good answer.)
Various publications will have strict rules about what diacritics are used and when. For example, The New Yorker always uses diaeresis. Each publication seems to have its own rules for bolding, headers, section numbering, hyphenation, capitalization, reference citation, and so on. And there is no definitive format.
I believe that diacritics fall into this category, as evidenced by their generally inconsistent use (though internally consistent within many publications).
Your premise is wrong. Homographs that are not homophones exist in a great many languages, and in a great variety of writing systems. Germanic, Slavic, Sinitic; Latin, Cyrillic, Hanzi; you name it.
To distinguish lead from lead, 易 from 易, замок from замок, Heroin from Heroin you have to rely on context. Some languages might try to help you out by using diacritics (Spanish, French, Greek) or stress marks (Russian), but others will not (Modern German, Modern English).*
When there's not enough context, all bets are off, but keep in mind that that is not some weird exception, but rather the default situation. Any sequence of characters in any language is free to have as many different meanings as people choose to give it, and is thus prone to being ambiguous with not enough context provided. (And remember how there are complete homonyms, where not just the spelling but also the pronunciation are identical. Yet everyone makes do with them just fine.)
Present vs. present is an example of an initial-stress-derived noun, which are extremely common in English. The thing is, these homographs in particular are exceptionally easy to tell apart, because one is a verb and another is a noun. You'll typically need very little context to tell what part of speech you are looking at.
As to read, it actually nicely demonstrates another problem still: we likely have the pair of homographs because otherwise we'd have a pair of different homographs. That is, the past-tense read actually used to be spelled "red", but that in turn conflicted with the adjective red. We have prior questions on that.
* And of course at the extreme end of this spectrum you have systems like Japanese, where every single kanji has two readings, by design, so as a complete layman I can't possibly tell how to read anything at all, until some kind person comes along and spells it out for me in hiragana. Yet lo and behold, the system is alive and thriving, and has been forever, and will go on to outlive me.
Best Answer
I regard coöperation as a New Yorker affectation, but it really a matter of style. In the UK it will commonly be written co-operation to match the Co-operative Retail Societies. The real difficulty is with the four-letter version: Harvard/MIT call their shop the Coop.
As for the others, this is a matter of anglicisation of loanwords and changes slowly over time depending on how useful the diacritics are seen to be. I suspect naive is now more common than naïve, and that the half-accented resumé is now used almost as often as résumé.