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People are allowed to use a phrase for its literal meaning instead of the traditional idiomatic meaning.

"beg the question" does not have a literal meaning. It makes no sense unless you're so used to hearing it used that way.

"beg" often means "beg for". "This situation begs for the question:" is a completely reasonable way to start a sentence.

Or to go with synonyms. Solicits the question. Entreats the question. These are the literal meanings of the words, and they work fine.