Strongly disagree. There are so many places where the browser itself provides a reasonably good user interface, and web developers fuck it up - scroll hijacking and history manipulation being two of the biggest examples. I suspect that one of the reasons we ended up in JS-hell is that HTML and browser built-in functionality lagged behind user expectations for so long. If browsers had offered the equivalent of AJAX and DOM element replacement early on, heavy use of JS might never have caught on.
The browser only reluctantly accepts its role is an application UI platform. Every problem, including the ones you describe, come from the disconnect between what a browser is and what it is used for. The browser is always going to lag behind user expectations so that's why I think it's the last place we should put that functionality.
Adding more high-level UI functionality is really in conflict with the idea of browser as platform. Other features, like WASM, are pushing the browser the other way.
(Consider Triptych [https://github.com/alexpetros/triptych] as the baseline for what browsers should have been providing since 2005 or so.)