Now, you could of course craft a page that would still work well on screen readers and that at the same time does the whole dog-and-pony show on more capable browsers. But in practice that doesn't really happen.
Many pages which are in fact just text pages once rendered simply won't render or will render very badly with javascript off.
This is also how I discovered what a clusterfuck the Android accessibility tools are. Talkback before Marshmallow is atrocious (as in very obviously buggy), I'm going to test the new Talkback now and see.
What you mentioned about accessibility features being available but not being used in practice is not only in the web. You get the same thing in Android and IOS applications as well. I have always wondered about how we can fix this, but to be honest, I have never found a solution, sadly.