The main feature of rust isn't borrow checking, the feature is
safe low level programming. Borrow checking is Rust's default way of doing this, but it's not the only one (the standard library has Reference Counting primitives built in).
Borrow checking is a way to make manual memory management safe, ECS works around manual memory management entirely, so it doesn't need borrow checking to be safe (which is also why it's popular in C++, which doesn't have a borrow checker) but because it's Rust, you have strong guarantees about the safety of it, while in C++ you can still shoot yourself in the foot if you don't use ECS the right way.
Also Rust is more than safety: https://steveklabnik.com/writing/rust-is-more-than-safety
