Asking for one for the entire web is not a good plan because it would exclude competition. That's where the flaw in the argument is.
And while it'd be nice if browser vendors could just go off and improve along (from a browser vendor's point of view), it absolutely sucks for every single developer and the users. Surely, you remember "this website runs only on...". This is exactly what you see in the apps market - applications only running on certain devices, locking in the users. Sure, for you as a developer it's convenient. For users, it's a bad idea.
It's important to distinguish the Internet from the collection of web technologies. The Internet is the thing that needs to remain open and uncontrolled.
The only other way to read that is that you're advocating splintering web technology into HTML-Moz, HTML-IE, HTML-Cr and so on. While that might make for a better developer experience for somebody who develops apps for _one_ of those platforms, it's a disaster in terms of interoperability. Which is kind of one of the key points of "The Web".
We were heading down that path for a while with browser-specific extensions, and it lead to large problems. For users, because they needed to have "just the right browser". And for many backend services, because actually extracting data from web pages required understanding all competing standards.
I care mostly about the users. The web of yore, with "best viewed with" stickers was a debacle in terms of UX.