> This shift towards using the phrase to mean "raise the question" makes it harder for a writer to tag a claim as being guilty of that particular logical fallacy.

No, it doesn't; the petitio principii fallacy sense is inherently intransitive in structure (with no direct object), the “raises the question” sense is necessarily transitive (has a direct object, specifically, the question raised). They are unambiguous (and the intransitive sense cam be rationalized as a special case of the transitibe sense where the unstated object is the justification for the original claim, which is convenient since otherwise that sense is completely opaque in terms of any relation between the constituent words in current English and the meaning of the phrase.)

So put more simply, what you're saying is that the reader can tell by the context. When the writer says "this begs the question", if that phrase is followed by an actual question, the reader knows the writer is using it in the newer sense. If it isn't, the reader knows the writer meant it in the older, logical fallacy sense. I understand that. My claim that it makes it harder still stands. The reader must use context to determine meaning when he didn't have to before.