Leaking isn’t really the issue, though I suppose Rust helps with that as well. Its memory sales pitch is more about memory safety, which is not reading or writing the wrong parts of memory. Doing that can have all sorts of effects, where the best you can hope for is a crash, but it often results in arbitrary execution vulnerabilities. Memory _un_safety is pretty rare and most prominent in languages like C, C++ and Zig.

Rust also has more information contained in it, which means resulting programs can actually be faster than C, as the optimizer in the compiler is better informed.