An all-Rust browser would make a big difference. Sandboxing is good, but won't close the gap with Chromium, which just invests too much money into software security to lose much ground to other browsers.
Agreed for the most part. There is Servo[0] which is Mozilla's playground for a Rust Browser. It's not really usable for day-to-day browsing, but it's a neat proof of concept. They are actively moving stuff from it into FF, and FF now requires rust to build. Google definitely cares a lot about security. It's great to see them embrace U2F so heavily, that even Chrome supports it out of the box. I'm not sure FF will ever become Rust-only, but if it did, it would take quite a while I think.