Preventing memory leaks isn't normally what people mean by "memory safety".

As an aside: a common memory management approach used in Zig is to have a dedicated memory pool for an operation and simply free all of the memory after the operation is over instead of freeing individual allocations.

This is simply untrue. Zig offers the same spatial memory safety as Rust does, and that is the kind of memory safety that prevents more dangerous vulnerabilities [1] than the kind Rust offers and Zig doesn't (temporal memory safety).

> if you don't free something manually it won't get freed

Rust also isn't free of memory leaks, and doesn't even pretend to guarantee that all allocations are freed. Lack of memory leaks doesn't fall under what Rust defines as memory safety (which Rust defines as guarantees it does provide, excluding those it doesn't).

[1]: https://cwe.mitre.org/top25/archive/2024/2024_cwe_top25.html - Rust and Zig's memory safety prevent #2 and #6 on the list. Rust, additionally, prevents #8. C prevents none of those.