Your advice basically tells them to get out of JS development because businesses continually hitch themselves to <JS framework of the year>.

This stuff comes up in interviews. Trying to avoid answering direct questions about a framework and answering with "Well I can learn it really quickly because I'm a good vanilla JS Dev" doesn't fly all the time. If you can't answer direct questions about a framework, they will pass on you if they get someone who can answer those questions.

It has nothing to do with marketing yourself.

What you described is a hiring problem. Marketing is knowing who your buyer is and finding creative ways to get their attention.

Found the MBA/project-lead guy. The moment you start working on management, that's the moment you stopped being a "developer".

I don't think that's the only interpretation. You can also work on moving into different parts of development. This problem exists everywhere, but is currently the most extreme in front-end web-app dev. Move the back end, ops, etc..