While naïve is less common than naive, it is not archaic; it's simply an alternative spelling that's less commonly used.

Actually, to my surprise naïve even seems to be gaining in popularity to the point it's about on-par with naive: https://books.google.com/ngrams/graph?content=naive%2Cna%C3%...

And that other words in English have unfortunate spelling is not really a very string argument. You can use this on anything.

> naïve even seems to be gaining in popularity

I wonder if this is the impact of technology. When written by hand, there's not much practical difference between naive and naïve. With English typewriters and English keyboards, writing naïve is tricky so people, presumably, just didn't bother. Now, however, a lot of written text goes through spelling correction so, if the spell checker wants naïve then it may automatically change it or suggest you do.

In my completely rigorous and scientifically valid testing of this assumption: Word corrects to naïve, Chrome text box flags naïve, Edge text box is happy with both and imessage suggests naive. So bit of a mixed bag.

> it’s not clear how to pronounce

Indeed, this is a universal property of English spelling.