> I dare you to construct a normal sentence in which the particular usage of "begs the question" is not completely clear from context.
I'd say that in every case that it is used in its classical sense when heard by person who uses it to mean "raises the question." Using "begs the question" that way is an actual mistake. One can have only heard "begs the question" used properly, but if you weren't familiar with the phrase, easily and understandably take it to mean "a question is begging to be asked", then go on to use it incorrectly.
Using the phrase "begs the question" incorrectly is probably only an hour younger than the phrase itself. Correcting someone about it without completely explaining its actual meaning (because you'd have to, at the least, explain the difference between formal and informal fallacies) is about a minute younger than that.
It's hard to make a case for it being language evolution if the incorrect usage is as old as the correct usage, and isn't growing any more than proportionally with it.
People being upset about being corrected about it isn't new either. People who use it correctly will continue to use it correctly, and people who use it incorrectly will use it correctly after they learn formal fallacies and can't think of a better, pithier way to describe that particular one.
Using it incorrectly, of course, is a sin akin to using an eggcorn (http://eggcorns.lascribe.net/) : everybody has misheard or misunderstood many things, and then misuses them. The problem with finding them is that one has to use them in a conversation with someone nice enough or brave enough to correct one.