Chrome might not be able to, but the website can, surely? Why not leave it to developers to properly handle state within their application (e.g. by using history and 'beforeunload' functionality) rather than second-guessing it at a browser level?

Then the problem would ALREADY be solved, because all developers would already be properly handling state within their application instead of second-guessing it at a browser level. But they don't.

It can and they know how to implement it. There is a pretty clean distinction of where the user can input some data.

The only thing it could do is alarm you for navigating away from any webpage that has any form that has ever had input put into it. Also, the website could intercept the "go back" event for some purpose. Should the browser fire an alarm then, as well? Either way, it would be a terrible user experience.

There's no notion of "unsaved" changes. There's the notion of form data that hasn't been submitted, which is entirely different. Many web apps don't use "submit" at all, ever.