harry potter - Was the fact that the foreign schools were non-coed important?

Is there any explanation for why the other 2 schools in the TriWizard tournament are both single-gender, unlike Hogwarts?

Was single-gender education normal in wizarding world with Hogwarts being the exception?

Was this some special intentional literary trick on Rowling's part or on movie creators'?

Here's the evidence from the movies:

Durmstrang Institute is boys-only:

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Beauxbatons Academy of Magic seems to be an all-girl school:

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