Language isn't logical. It's a bricolage of things people have done to communicate. It's a mash-up of many different tools all trying to accomplish a hundred different things, and if people can't find a handy screwdriver, they may successfully use a butterknife instead.

It's not incorrect, and calling it that is exactly the misguided pedantry referred to in GP.

> I'm not opposed to linguistic innovation if it makes the language more elegant or more expressive

The intransitive sense of “begs the question” does exactly that, and I explained how it does that in GP. Also, its been in common use long enough that it is hardly "innovation”; the persistent pedantic struggle against it is a reactionary struggle for linguistic regression. Which might still make some sense, if the usage was one which created confusion or obscured meaning, but its not.

Having said this, on the internet, I must now defend it.

to beg in conversation is of course more energetic than raising or prompting. When you beg it is urgent, a question that has been raised can be tabled for later, a prompt can be ignored as we point at a different reporter we know is more likely to ask about how this affects the First Lady, but if the question is being begged it demands an answer from us.

To beg calls forth the image naturally, for those who think in images, of a beggar. A beggar has moral urgency, they need what we have to give, and that moral urgency of the image is transferred to the question implied by the subject of discussion.

To prompt or raise a question have absolutely no visual analogue, they are lifeless, bloodless, and should be buried before rotting.

Why do you think that this more common usage of beg the question has come into play? It's not (necessarily) ignorance, I believe the cause is that the phrasing in English far better supports what is wanted and this allowed the phrase itself to spread among the population as a tool for expressing thought.