Are heteronyms unique to English and why do they exist?

Solution 1:

We have many heteronyms in our language because English spelling is so illogical. Other languages do have heteronyms. For example, googling "French heteronyms" turns up the pair

des fils: /fil/ some thread,
un fils: /fis/ a son,

which only works because the French spelling of un fils is irregular.

Solution 2:

French has d'eux (of them), and deux (two). Borderline case, admittedly, but famous in legal circles for the will that left "a chacun d'eux/deux mille francs" leaving the lawyers to argue whether it was an apostrophe, meaning each heir got a thousand, or a speck, meaning each got two thousand. And that is why old-fashioned English courts still do not use punctuation.

(That's the story I heard, and I'm sticking to it)

Oh, all right then: there are far more possible meanings than combinations of sounds or letters, so some combinations get used more than once. English, having a larger vocabulary than most languages, has more of such 'multiple-uses' though most are either written the same with different pronunciation (homographs) or vice versa (homophones).