yes we have enough proof of that concept... I do not believe you. It's a urban myth that rewriting always make things faster. Especially when looking at a C(++) code basis. Rust will maybe make the code safer but I doubt it will make it faster.
Improving the design is part of a rewrite, which would make it faster, even if the rewrite was in C++. Sufficiently large, old projects (and Firefox certainly qualifies) tend to accumulate a lot of gunk and design choices that used to make sense, but don't any more.
Rust also allows one to safely use patterns that one couldn't use in C++ without screwing things up, thanks to the borrow checker. And quite a lot of Firefox is written in Javascript, which definitely would be faster when rewritten in a compiled language.