I doubt they'll get noticeably better performance (the main GNU tools are already very optimised). I'm not sure they really lack in resilience. And I don't think memory safety is a big factor here.
Maintenance is definitely a big plus though. It will be much nicer to work on modern Rust code than ancient C.
https://www.youtube.com/watch?v=5qTyyMyU2hQ
In an interview with FOSS Weekly, Sylvestre Ledru (the main developer, who curiously has a background working on Debian and Firefox, before ending up getting seduced by the clang/LLVM ecosystem), firmly states "it is not about security".
i am surprised by the implication
Every proprietary Linux OS (such as most Android phones) uses busybox, at a slight disadvantage to them, because they can't handle using GPL3 coreutils. Now they'll use the MIT-licensed drop-in replacement coreutils.