Indeed. A good example in English is Mary/marry/merry. Many speakers pronounce all three words identically, but many speakers distinguish them. Should the spelling be unified? Probably not, because they are three separate words that might sometimes sound the same in speech. Simplifying spelling removes any way of distinguishing them.
English is filled with homophones, and while you can almost always figure out which variant is meant through context, in writing the opportunity is reduced. (You can't ask a book a follow-up question.)
I do think this is a great point but I do think the idea is fun to consider anyways. My first thought would be some (silent) {super,sub}script symbol/letter to indicate distinction between them. Obviously this feels like we'd be right back where we started but if every non-homophone was neatly standardised (and, as my sibling comment pointed out, every homonym made unambiguous) that seems promising! This is, of course, operating under the assumption that homophones are primarily edge cases (or that the other words in the homophone group are not often used in the same context, or at all).
Minimal research turned up two lists. One only lists groups of n > 2 (88 triples; 24 quadruples; 2 quintuples; 1 sextet; and 1 septet) [0]. The other is for British English (441 groups) [1].
Your example, by the way, is a particularly interesting case! From the Wikipedia page [2]: 17% of Americans (primarily in the Northeast and most clearly in Philadelphia, New York City, and Rhode Island) pronounce each distinctly, with a further 26% merging only 2/3 pronunciations. Accordingly, their distinct IPA pronunciations are /ˈme(ə)ɹi/, /ˈmæɹi/, /ˈmɛɹi/, respective to your ordering (the last, merry, is the one we've converged on). More frustrating still, the list of "multinyms" in [0] excludes this example so it's especially difficult to know how many there may be in practice.
Another effect is that the sound variety in the language was reduced. The new alphabet has "n" for both "ŋ" and "n" sounds. Now, in year 2020, no one spells out ŋ. See "taŋrı", "seniŋ", etc.
That's not true I am afraid. Turkish borrows majority of it's vocabulary from Arabic, Persian, French and English. Wovels in those loan words never match the sounds. For example the word "hala" can either mean "aunt" or "still" depending on how long you sound the first a.
For some reasons that I don’t understand I think that spoken Turkish sometimes reminds me of Russian.. Not that I’m fluent in any of them but I usually can recognise Russian quite well and understand some words.
Learn the phonetics of each letter, and you can literally speak any word.