Google has some pretty good data on this: https://security.googleblog.com/2022/12/memory-safe-language...
As for Firefox, the CSS engine was rewritten to be parallel, among other improvements (new wasm compiler, new parallel compositor) that would have been challenging without Rust: https://wiki.mozilla.org/Oxidation
> but that's not really provable in any meaningful way.
Can you prove that Rust didn't make developers more productive?
Also, that there are less memory bugs in Rust then in C++ is just common sense and pretty generally accepted. It doesn't need to be proven again for every project.
> After seeing the Firefox situation
The situation where more and more code is written in Rust because most people prefer it?
Multi-core CSS engine and GPU-accelerated rendering in Firefox are in Rust. Without them Firefox was really behind in performance (if you're unimpressed now, imagine it being way worse).
If I'm not mistaken, the first stable Firefox releases including notable usage of Rust code came out in late 2017. So that's about 6 years of Rust in Firefox.
From a Firefox user's perspective, I can't say that I'm impressed by it.
Building Firefox from source is more involved than it was before. As you mentioned, additional tooling for Rust is required in such a situation.
I haven't really noticed any real Firefox feature, functionality, or performance improvements that I could directly attribute to the use of Rust.
It also doesn't seem like using Rust has allowed the Firefox developers to be significantly more efficient or productive than they were before.
Maybe an argument could be made that some security issues, for example, have been avoided thanks to Rust, but that's not really provable in any meaningful way.
After seeing the Firefox situation, my expectations for the use of Rust in the Linux kernel are pretty low.