I recall statically compiling Rust to be a big pain (like, actually statically compiling, no dynamic dependencies on libc in Linux). I assume this is all the more true with arbitrary C dependencies?
If you have no C dependencies, it’s simple: you ask for the musl libc, and you’re done. It is not more onerous than go.
If you have C dependencies, then it does become a pain, depending on how well those dependencies' -sys packages interface with whatever build system they use.