tmux doesn’t really gain anything from memory safety because:
1. anything running in tmux already has execution rights and typically for the same user as tmux anyway.
2. Anyone who wanted to exploit tmux could just run ‘tmux -C’ and automatically get access to literally every interaction within tmux.
3. The software itself is already damn stable. I've never had it crash.
If you’re worried about someone exploiting your terminal then tmux is a terrible option, irrespective of whether it’s with written in C or Rust. And I say this as someone who absolutely loves tmux and uses it every day.
[edit]
And if you're worried about non-security related bugs affecting UX, then a rewrite in any language, regardless of the language, is a worse solution if your application has already been battle-tested for close to two decades. You're much better off creating something entirely new instead of porting code from one language to another because at least then you have new ideas instead of the same application but with new bugs in different places.
I don't say this because of some bias that Rust fanboys will assume I have. I love memory safe languages and think Rust is a great option for new projects. The point I'm making here is that a rewrite doesn't gain much for tmux SPECIFICALLY because tmux is already extremely stable.