Why would that be any better? The only thing the page displaying in any browser needs to be aware of is how big the viewing window is, and the DPI. With those two pieces of information, you can have anything that runs in a browser present a useful interface.
That way content can handle all the edge cases that different screens can throw at them. And different browsers can handle things like text sizes the way they want to.
You don't want to have to make individual websites cater to individual screens or browsers. There's just too many of both. The interface between them needs to be a loose coupling.
A better way to say what I was getting at is that a web browser that finds itself with a silly window size might better serve the user by only using a portion of it for the viewport.
This way a page with no extra width styling still gets presented to the user in a sensible fashion. It's probably a looser coupling than insisting that every page anticipate and handle the screens it might be viewed on.
The browser shouldn't be dictating how the web works. It's the creator's job to manage the complexity of presentation, you can't just push that responsibility onto your tech stack. The domain and expected use cases for web apps is just too broad for any browser to be making decisions like this.
That way content can handle all the edge cases that different screens can throw at them. And different browsers can handle things like text sizes the way they want to.
You don't want to have to make individual websites cater to individual screens or browsers. There's just too many of both. The interface between them needs to be a loose coupling.