Well, em dashes are commonly used in pairs to make distinct logical clauses; where one is used, two often are. So em dashes per word count isn't a great indicator of LLM use, particularly considering that different subject matter warrant different amounts of distinct clauses—most noticeably when in lists.

Some examples in conversational English:

• "I work with him—he's my employer—we met at a café in town."
• "...Carl is in Phoenix, Arizona; Jesse—a friend of mine—lives in Elmira, New York; Geoff is in Toronto..."

All that said, LLMs do use em dashes slightly more than I in the majority of cases.