I like your comment for the most part, but:

obviously comes from a mishearing by someone who didn’t read books

This is assumptive and prescriptive. The link I sent demonstrates that it’s been used extensively and for a long time by people who not only read books, but write books. I’m on board that “set foot” is the better phrase and likely to be the earlier one, but trying to dictate which is correct is - respectfully - a fool’s errand.

“Set foot” might be better established (and sound better), but “step foot” is not new.