Lets reverse that - why write in a language without a GC when you can write in a language with a GC? Rust's advantages shine when it's time to go low-level, but being without a GC is a disadvantage otherwise.

This application isn't merely 'performance-sensitive', it's a very particular form of performance - performance over network (I assume that's the main bottleneck here). Better write in a ecosystem all-but-officially optimized for networked applications rather than lose developer productivity dealing with low-level stuff.