This gives too much control to the browser and away from users and developers. And the browser is by someone who has too much control already. It is hard to ignore how this will play with AMP for the worse. Allows almost arbitrary branding display of URLs.
I agree that host parsing is difficult and many big sites are famous for crap URLs. But hiding the good parts makes the web lose the advantage that it has vs apps. Where people can't know that a location inside an app exists. Here it is explicit that you're somewhere inside the domain. Now it will be "Somewhere inside domain.com clicking such menu and that option"
I'm all for better rendering of the hostname. Like #Firefox does. But not hiding the path and rest of the URL.