This lossy mingling of expressions that sound similar is a natural process always present in the evolution of a language. Giving up is a correct and healthy response imo.

"Begging the question" is a great example - its intended meaning as a specific fallacy descriptor lose to face-value interpretations that are "wrong" but also extremely fair for somebody to make. All this means is that "begging the question" is a weak name for the fallacy, because if you don't know what it means, a wrong assumption is easily available and contextually often seems to fit.

The language crushing out these expressions is a feature. Better all around to say the argument is circular or it assumes the conclusion. Doing those things may _actually_ "raise questions" as well as "begging the question" which makes things even worse.

It's not the fault of the casual language users that this expression is poorly understood, it's just bad naming in the first place.