Every radio and TV news reader and commentator in the US has been saying "beg the question" for at least a decade.

Once I started noticing, I soon realized that in the 21st Century they almost *never* say "raise the question."

To "beg" seems to be more colorful than to "raise."

When people really mean "beg the question," they now say things like "evade the question," "overlook the question," and "dodge the question." Of course, they've always said these things too.

Since to "dodge" the question makes more apparent sense than to "beg" it, and to "beg the question" superficially seems to mean to "demand that one ask," the new pattern of usage is ineradicable.