Yup - "STEM jobs pay well" is just wrong at this point. Neither Science nor Mathematics pays worth a damn, what people actually mean when they say this is "go work in technology or engineering".
I think Academia is not paying that well. I think a lot of these post-docs could make a lot more in industry, no? I think if you are willing to sell your soul to the devil, most STEM pays pretty dang well...
I think this is only partially true. It's really a case of what you worked on, where you worked on it, and who you did it with.
For example: a lot of Biochemistry and Dev Bio these days relies at least in part on so-called next-generation sequencing. If you happened to work on a project where you worked with that technology, there are lots of well paying jobs out there for you. If not, it might be harder to find one, but again it's very person-project-location dependent.
Of my graduate school (PhD Biochemistry) cohort, I don't know anyone who doesn't have a job they're happy in. Some of them went postdoc, some went to industry (maybe 50-50 at this stage), and I have no doubt those who stayed in academia would have no problem finding a job in industry. That said, I went to a strong program in an area where there's a lot of Biotech, so that helps.
As for me, I left academia and am now a hybrid data scientist/biochemist, I'm fortunate to have a decent salary and a job I love. Was the PhD worth it? I wouldn't have this job if I didn't, but I don't know. If it wasn't it's mostly because a PhD was a huge opportunity cost for me I think.
Yeah I never understood the "get a job in STEM" anecdote. As a designer/developer I don't really place myself in the STEM category. A more accurate anecdote would be "learn how to program a bit, figure out how to solve some problems, take a bunch of different classes, work for a few years learning how to do real world things and you can easily pull in $80k + in any city in the US". If money is your main goal then I don't see a better path in any other profession.