If you go by volume, you may well find that the theoretical definition you're referring to is outnumbered by the practical reality. I definitely wouldn't assume that reality matches theory.
I'm going by my personal experience as a PM. To be fair, whenever I talk on a PM panel I tend to be the odd one out.
For example, I tend to be the guy on the panel all the other PM's hate because I taught myself to code so that I could have deeper empathy for how my engineering teams work and now I advocate for all PM's needing to be at least moderately technical.
Rocking the boat certainly doesn't make you popular haha
Yes - totally agree. It's a tricky job, and there are real product people, of course, but I think there has been a bit of a migration away from the slightly unfashionable "project manager" into roles such as this one, flooding it.
Also, Product has in some places gone from a valued member of the team to a ruling class, with all the faux problems that generates.