This came up recently somewhere else and my two cents:
1) The best role for LLMs in ATS is in rewriting all resumes consistently in a style which matches the biases / "likings" of the reviewer (Humphry Bogart, Exene Cervenka, Kermit the Frog). Applicants guessing at this merely gives them a better shot at being mistakenly included in the cohort which adopts the preferred voice "naturally". If this "liking" is what resumes are supposed to be judged on then where's the math, it's all a smokescreen for bias innit?
2) Some ATS needs to be the first mover in allowing applicants to download / upload a JSON BLOB of all of their info. I'd recommend cryptographically signing it (and calling it a "service") on download like DKIM, and I think a bunch of things would emerge with that.