I think this is a good idea.
The next one would be to also decouple the visual part of a website from the data/interactions: Let the users tell their in-browser agent how to render - or even offer different views on the same data. (And possibly also WHAT to render: So your LLM could work as an in-website adblocker for example; Similar to browser extensions such as a LinkedIn/Facebook feed blocker)
Why would Facebook or LinkedIn ever give you this?