A dynamically typed Lisp has virtually nothing in common with Rust. A cached heap can benefit literally any language which is why it's an optimization found in some programs written in C or C++ as well.
Also, Rust binaries have been of comparable size in the past. Check out this question where someone asks why Hello World is 3mb even in release mode:
https://stackoverflow.com/questions/29008127/why-are-rust-ex...
This 3mb doesn't have any cached heap, doesn't have any garbage collector, doesn't have support for high quality exceptions and doesn't have much in the way of a cross platform abstraction, whereas the Clojure-as-native binary has all of those and more.
There's a giant pile of things you can do here to try and reduce Rust's binary size:
https://github.com/johnthagen/min-sized-rust
... but as you can see, it's a lot of work.
Rust gets great press and HN is flooded with "let's do it in Rust" type comments. But I think sometimes we need a reality check. Rust is an extremely different language to most others, even C. The combination of the borrow checker+everything async is not obviously better than everything else, not even in the low level domains even though Rust is deservedly picking up loyal users there. The moment you care about development speed i.e. for the sort of apps Clojure was designed for, you're going to be better off with a GC and a strong runtime that abstracts the platform well.