Leaving the HTML/CSS rendering alone for a while, if you could decide, what native features would you like to see in your browser that isn't already there?
— Attaching persistent notes to parts of the page.
— Bookmarks that let you add a comment.
I've come to desire that all desktop apps had a dedicated persistent scratchpad attached, it feels great to see your ideas and links, go you! and trails!
* Better reading modes
* Better selection modes. There have been a lot of tools/extensions made over the years to help you do things like extract every image on the page or copy out a single column of values from a table and it might be time to think of making some of these native features.
* Great screenshot ability: Firefox has this worked out pretty well now enabling you take the picture of the entire page natively rather than having to install a 3rd party extension
Limit each site to a megabyte. If it wants more, it can wait until I approve a doubling. Each doubling needs my approval. For example, upon hitting 128 MiB, the site should freeze up until I give the OK for going up to 256 MiB.
Limit each site to a single thread. Let me approve more or just force the site to live within a limit.
Limit each site to running in the foreground. (only the visible tab of the currently focused window runs) If I really want something to run in the background, let me indicate that with a right-click menu on the tab.
Many of these could even be pre-bundled with the browser.