Because if they're not owned, then how do you know who is who? How do we independently conclude that yup, microsoft.com goes to Microsoft, without some central authority managing who's who?

It's first come first served which is a bit biased towards early adopters, but I can't think of a better system where you go to google.com and reliably end up at Google. If everyone had a different idea of where that should send you it would be a nightmare, we'd be back to passing IP addresses on post-it notes to your friends to make sure we end up on the same youtube.com. When you type an address you expect to end up on the site you asked, and nothing else. You don't want to end up on Comcast YouTube because your ISP decided that's where youtube.com goes, you expect and demand the real one, the same as everyone else.

And there's still the massive server costs to run a dictionary for literally the entire Internet for all of that to work.

A lot of the times, when asking those kinds of questions, it's useful to think about how would you implement it such that it would work. It usually answers the question.