Any reason to use or teach `…` substitution for new development?

Since back-ticks are often used, it makes sense to teach this syntactic construct.

Of course, $() style command substitution should be emphasized as the default style (and standard conforming construct).

Why are back-ticks still popular? Because they save one character in typing, and they are arguably less heavy on the eye.

I would not use them for programming, and teaching the use of backtick substitution in shell scripts as obsolete is fine (this seems to be the consensus). I don't think they're inherently evil, however, and (at least judging by your average tutorial to Linux command line) they are still frequently used in simple snippets/one-liners where they probably won't be nested and things you're only going to do once.

See Command substitution: backticks or dollar sign / paren enclosed?.