When xhtml was popular internet explorer was a major blocker for using it properly. I never saw xhtml served with the proper content type at the time.

I don't see a reason to mix html and xhtml today. It will only lead to problems. (I.e using self-closing tags and & mismatches in urls)

If you use <div/> in html the browser will just ignore the end / See https://jsfiddle.net/sw8j9fo2/