In the past, only Mozilla cared about what the W3C said, and they built Firefox on the idea that interoperability by following the standards is the way to go. Not that long after Apple initiated Safari, and led Google to their own browser initiative.
All this because Mozilla, the insignificant actor of the all IE time, decided to follow W3C.
You're not totally wrong telling that W3C doesn't mater that much, but browsers are what they are today because of W3C for a good part, and it still have a very important place in the browser game.
This is pretty much the opposite of how things went down.
If browsers followed the W3C, we'd be living in XML utopia (XHTML2, XForms, XLink, XEvents, etc.). In 2004 a group of implementers (specifically Mozilla, Opera, and Apple) proposed to the W3C to focus on web applications by evolving HTML and the DOM, but were flat-out turned down, and had to go off and form their own standards organization---the WHATWG. Today, that is where much of the foundational work of the web platform is still done: https://spec.whatwg.org/
