Some absolutely incredible ideas have been discussed about a potential new engine (Servo based) that could be privacy-first / lightweight / fast / bloat-free. This would require rethinking the web in a retro-compatible way, and here again I've heard of some very smart ideas.
… but who's gonna lead that? And where will the money come from?
There are organizations that give grants for open source development that impact people, and a browser seems like an extraordinary good fit, e.g.: https://nlnet.nl/
Additional, asking individual users for funding is very wise (like what Signal is doing[1]). Sending a clear message of why funding is needed is also important. I'd personally be willing to put some recurring funds into this, and I'm sure many other people in tech would care about this too -- pretty much the same of us that are pissed at where Firefox is heading.
I care about this subject a lot, I'd be interested in corresponding with people with the actual expertise to work on it, want to shoot me an email? hugo at whynothugo.nl
Hard.