The thing is, "beg the question" as it is used in everyday language is much more transparent and easier to understand than its 'proper' usage.

If you want to describe that specific fallacy in some way, there's a lovely phrase for that which already exists, describes the fallacy better, and uses fewer words - "petitio principii".

"Beg the question" used in this sense strikes me as redundant, inaccurate as a translation and a description, clunky, and pointlessly confusing. I hope its misuse is not actively fought, and that people who wish to describe the fallacy find a better way of doing so.