What Rust helps with is memory safety, which is stuff like dangling pointers and use-after-free. Memory leaks are not a safety issue, they're an efficiency issue.
> Why are people so crazy about Rust?
The whole memory safety thing isn't actually the reason so many people love Rust. In the Rust 2024 community survey, 82% of users agreed that "Rust allows us to build relatively correct and bug free software." Memory safety is part of that, but there's a lot more to it.
So, for example, while Rust does not guarantee the lack of memory leaks, it does make them relatively hard to produce by accident in the first place. This is due to the intersection of a few different parts of Rust's overall design.
