It's typically only used when there's a person who's unknown, so it's less intentionally "generic" and "generic because s/he have become sex-specific."
Over my lifetime "he" and "she" have become increasingly equipollent in all contexts, with the external mandate by neo-prescriptivists that the *new* rules of grammar are the ones that must be followed. When I was young, "he" was unmarked wrt sex in certain contexts. People stopped paying attention to the contexts--or, as is often the case, when it's advantageous to be context-blind for purposes of power expression through language manipulation, forbade others to pay attention to the contexts. Find something to be offended at when none is intended (or even recognizable 20 years ago), project the intent to offend on those with no such intent, and then require that people not offend in order to not be immoral. Either way, "they" had been around for ambiguous contexts for a long time.
That's different from indefinite "they" as in "You know what they say," where there really isn't a referent beyond "people" or "somebody somewhere." Compare "They say that the ends always justify the means, but I don't buy it" versus "Some student wrote a racist comment on the whiteboard--too bad they didn't sign it so we'd know who to punish."
The same kind of power expression is seen in linguistic imperialism by WEIRDs and their acolytes, where "because this is how it works in English it must therefore work in the exact same way in all other languages" is the reasoning. It was a silly idea back in the 1600s with the ur-prescriptivists' dicta for how English must be like Latin (it's bad to even accidentally split infinitives, for example). It's not just a silly idea when old white men do it. Of course, it seemed wise and prudent in the 1600s, I guess.
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