The jobs aren't rare, but they usually aren't paying as much as an experienced specialist (and certainly not paying more, despite the job covering a larger knowledge area). Since experienced generalists are always still going to have some areas they have more knowledge in than others, I think it leads to them applying for the higher paying specialized positions.
I’m an experienced generalist looking, and I can assure you about the job postings.
Totally agree on the huge impact, et al. And for available jobs without a job posting, this remains as you say. But when a hiring manager goes to HR/recruiting and a job posting is generated, it is never for a generalist.
So, an experienced generalist has to skip over specific postings, simply look at who is hiring at all (or growing headcount as evidenced by other data points), and find a way in to pitch themselves.
Except for a very narrow set of hyper-specializations, pretty much every experienced hire varies from posting, in my experience. Sometimes you need to hire one of the worldwide N top in X. You probably don’t post this. Most of the rest of the time it’s more nuanced.