WebGL has been working fine for years...?
Not really.
Since the browsers black list GPUs and platforms where they have issues, as author you don't have any guarantee how the users will get to see your site.
Additional not all GL ES features are exposed to WebGL.
Depends on your definition of fine. In certain cases it would crash browsers on load, in other cases it would deliver a solid 60fps. I think 3d on the web does need a bit more polish so that it's a good experience universally.
The Unity engine has been outputting WebGL builds for years, and having played a bunch of them (and deployed a few myself), I've never once seen a problem that didn't exist in other builds of the same game
"Mostly works, sometimes doesn't" is the perennial state of accelerated 3D on the desktop. WebGL just exposes it as-is to JavaScript apps.
Kudos to the good people working on it!