To me they come off as faddish, with many writers using them where commas and semicolons would have done just as well. I think their popularity stems from teh fact that provide the sense of a personal aside from the writer, allowing them to be more expressive while clearly delineating the personal or contextual remark from the main flow of the prose. No doubt this works for a lot of readers, but I find it tedious.
You can restructureany sentence to use fewer forms of punctuation -- but if you do that, you'll lose nuance. And nuance, in writing, is a very fine thing.
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.