Sometimes the loss of an awkward construction is a gain for language.
"Begging the question" was never a very good choice of terminology -- a half-baked translation from the Latin petitio principii. You might as well use the Latin because you have to know what the term means to have an chance of decoding its meaning; the words give no clue. "Asking ill-founded questions" or "asking premature questions" would have been better.
"Begging the question" has *always* misled most readers and hearers, and we're better off with the new meaning, which *everybody* understands (although many dislike).