Earlier quoted context omitted.
I think you framed your anecdotal evidence as supporting the OP's statement, but also that you misunderstood such statement; and you actually present evidence against it. If companies find it hard to reliably staff generalist positions, _and_ you're a generalist as you claim, then you would find it _easy_ to get a job.
It's strange, but I think at least some companies find it hard to staff positions, while also at the same time ignoring/rejecting suitable candidates. Case in point - I'm a generalist who can very credibly claim very significant expertise at two disconnected areas (compilers and distributed systems), plus some startup/ product management expertise. I saw a job listing here for a startup that needed both of these and…
I have seen three approaches to limit this. First being to stay super field specific but implementation general, but not keyword void. Second, is to go super rabbit hole on every keyword/tool/language/platform you have ever worked with inside the field.
The third approach is to have a type one resume with a type two cover letter. That approach has usually been the most consistent for callbacks in my circles, and allows for your rabbit hole to be of the same type as the job description.