If languages were fully practical — the way most people think of them — they wouldn’t include idioms. Thus idioms constitute a mystery. No one knows why they exist,

My guess is that someone knows why idioms exist; there just isn't a consensus. That's not the same thing as no one knowing. (By exploring their psychological impact, doesn't this article provide a reason for idioms to exist?)

IMO, idioms exist because they paint pictures worth 1,000 words. They are virtually all metaphors. Try to deliver the message "beating a dead horse" in fewer words. Idioms are allusive, and allusion incorporates volumes by reference.

Metaphors are not "nonsense"; they are answers to the question "what's it like?" Take one example, "build a fire under." It means to impart a sense of urgency. But we want to connote not just that the urgency is there, but that it is irresistibly painful and so must result in action. The idiom says more than its "translation." That seems to me completely consistent with natural selection, if only at the meme level. Idioms out-compete their dry counterparts. (Does "dry" in that sentence make any more sense than an idiom? Is it a one-word idiom, in logical terms?)