Rust is unsuitable as a replacement for C because its memory management is poorly thought out (ie. its a joke). Here's the relevant paragraphs from the Rust FAQ. Really?
"Rust avoids the need for GC through its system of ownership and borrowing, but that same system helps with a host of other problems, including resource management in general and concurrency.
For when single ownership does not suffice, Rust programs rely on the standard reference-counting smart pointer type, Rc, and its thread-safe counterpart, Arc, instead of GC.
We are however investigating optional garbage collection as a future extension. The goal is to enable smooth integration with garbage-collected runtimes, such as those offered by the Spidermonkey and V8 JavaScript engines. Finally, some people have investigated implementing pure Rust garbage collectors without compiler support."