If the point is to easily be able to find work (which was the parent's emphasis), then yes, you need to learn the popular frameworks. No, it's not required for building your own web app, but companies use them, so they'll expect you to be familiar with them.

Where are you based? It seems like in most places it's an employee's market right now (assuming you work for an employer). Given the diversity of front-end frameworks and how new most of the trendy ones are, I find it extremely hard to believe that anyone who's any good at front-end development and has a decent track record to prove it will be short of work any time soon, even if they don't have a full complement of buzzwords on the resume. And of course it's certainly not necessary if you're doing it for your own business or if you're consulting/freelancing and have your pick of tools.

Portland, OR. I think you're probably mostly right with regards to frontend development. All my experience applying for non-contract work has been for backend positions, and I know for a fact that I lost at least two potential jobs because I didn't have the right language/framework on my résumé. But just based on my limited searching for frontend positions, it seems like companies do expect you to know at least one well-known framework really well, even if it's not the one they use. So you shouldn't need to master all of them, but you should definitely be familiar with their patterns.