"begs the question", like using "literally" to mean "figuratively", is so widespread that is is difficult to call it an incorrect use of language. However, both constitute what I consider a dismal use of language. (But for different reasons.)

"literally"'s conversion to meaning its opposite represents a loss of meaning in the language; expressiveness dulling into useless ambiguity.

"begs the question" isn't a term that expresses the underlying idea effectively, it merely indicates a failing attempt to sound educated.

In either case, I prefer to educate people on how to use language less dismally. This does make me a pedant.

I prefer this discussion of the meaning of the term: https://languagelog.ldc.upenn.edu/nll/?p=2290