The em-dash has indeed been around for centuries, but the fad I refer to is its overuse in contemporary American prose. IF you look at Google Books n-gram viewer, you can see it went through a surge of popularity over a few decades that then fell off sharply.

https://books.google.com/ngrams/graph?content=%E2%80%93&year...

It's also notable that the em-dash is approved in American Manuals of Style, while discouraged in British ones. I was unable to find longitudinal data for the em-dash's use in magazines, blogs etc., but AI summaries suggest it's 3-4 times more used in those contexts than in news reports.

Like strawberry ice cream or apple pie, nuance is certainly a fine thing; but a surfeit of it becomes cloying, and the antipathy toward the omnipresence of the em-dash in LLM-generated prose, along with other kinds of literary expression like contrast and comparison, suggests to me that people have had more than enough of it.