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Thank you! I think I was actually corrected on that once before, but maybe this time it'll stick =)

I feel like at this point common usage has moved so far away from this that it’s almost not worth trying to reel it back in.

A nice substitute might be begets. It is so similar, I wonder if that is where the confusion arose to begin with.

See https://languagelog.ldc.upenn.edu/nll/?p=2290 for some details. I would summarize by saying, there were words involved (i.e. the Latin "petitio" and Greek "αἰτεῖσθαι") that have multiple meanings (a modern analogue being "plead", which can mean "ask"/"beg", but can also mean "plead to the court [some statement of fact]"—i.e. to make a claim), and the word "beg" comes from a translator selecting one of the wrong meanings. Also, "the question" is really a poor choice to mean "the original point to be proven"/"the conclusion"/"the point in question".

I am strongly against prescriptivism telling people that a bad translation that makes no sense is correct. I recommend "assuming the conclusion" as a correct name.

This literally begs the question whether the prescriptive approach is to be preferred over the descriptive one.