Security is a factor everywhere. And C is everywhere. There's not going to be a "rewrite everything in Rust" project until after there is some legit penalty for selling / offering software in C that could be more secure in another language.
I think Mozilla got it right when they abandoned the effort to rewrite the entire browser in Rust and instead focused on analysis of which modules needed priority rewrites. If a module has historically had zero memory-related bugs, then there are other higher priority things to spend time on.
That said, Google Project Zero should have had Brotli on their radar. Hopefully they still have people and resources.
I’ll point out that Servo was always a research project — any thought of it replacing Gecko was an incredibly long-term stretch goal. It was _a lot_ more interested in “can we write a high-performance browser engine in Rust” (there’s a reason why it significantly predates Rust 1.0 — they were very much developed together!) and “can we implement parallelism in places where browsers historically have not” (because you have more guarantees of safety).
Chromium _has_ been replacing certain components with ones in safe languages, and it seems like that will continue slowly (with integrating them into the existing codebase, with web compatibility risk of any changes in behaviour, with the risk of performance and power regressions).
Asterinax. RustPyhon. PHP 8.5 rewrite in Rust. FFMPEG and Qemu might follow soon.
It's inevitable.