Rust is definitely a significant and important project. That said, Firefox's peak market share was a little over 30% of desktop browsers (in 2009 so they weren't yet a sideshow), while Rust isn't even currently in the TIOBE Index top 20 (can't find any easy way to see a peak position sadly).
More importantly though, we have other Rusts. Rust has half a dozen competitors and essentially nobody thinks that making a robust new systems programming language is an unachievable goal. Firefox is the only non-profit browser engine we have and most people consider it an impossible undertaking to develop a new one from scratch at this stage. Indeed, Microsoft recently tried before conceding defeat and switching Edge over to Chromium's Blink.
I'm thinking of Crystal, Nim, Zig, Odin and (ignoring that the topic at hand is avoiding Google having unnecessary control over things) Go. I'm aware they may not share Rust's exact feature set; Crystal is the only one I've used, including Rust itself. That comment was intended to illustrate that this is a field where attempts are made regularly and manage to achieve some measure of success, relative to browser rendering engines where I am only aware of a single (proprietary, incomplete) attempt in recent years: Flow.
Rust was supposed to be the basis of servo, a truly awesome engine that should have been under the hood of Firefox long ago. That should have been the best thing to come out of Mozilla.
We got some of it: the Rust language and Quantum. I would say the only two good things that Mozilla did in the last 10 years.
Finally, in 2020, the Servo and Rust team got the recognition they deserved, they got laid off...
It is almost like the old joke with the rower, where on a boat race, a team of eight people rowing and one steering beats a team with one person rowing and 8 steering. The losing team change its structure, now with a complex hierarchy but still a single rower, who eventually gets fired.
More importantly though, we have other Rusts. Rust has half a dozen competitors and essentially nobody thinks that making a robust new systems programming language is an unachievable goal. Firefox is the only non-profit browser engine we have and most people consider it an impossible undertaking to develop a new one from scratch at this stage. Indeed, Microsoft recently tried before conceding defeat and switching Edge over to Chromium's Blink.