I haven't worked through the grunt work myself, but I'm fairly certain it's basically not possible to design a completely fingerprint-proof browser so long as a browser includes a programmable Turing machine via Javascript, not to mention network request statistic info etc, all of which are used by completely legitimate websites to improve their experience & performance.

Modern ML can fingerprint you based on your mouse movements. Good luck selling a browser without mousemove events.

The vast majority of web sites don't need mousemove events except to enable bad UI design. The exceptions that are trying to implement a desktop app or video game inside the browser can ask for permission. It's not at all hard for users to make the one or two clicks necessary to grant a domain permission to use the bundle of advanced features it is requesting, and it gives them a reasonable opportunity to provide informed consent before a website starts monitoring their every move.