"This begs the question" is same as "This raises the question" – What is the logical fallacy in how it is phrased?
No it isn't, that is a common error in modern English. Raising the question means bringing a question into focus. Begging the question means to assume the conclusion is correct in the premise.
https://www.merriam-webster.com/words-at-play/beg-the-questi...
which seems to indicate my usage is quite acceptable in modern English.
That information is also present in the Wikipedia link.