Don't Rust and Go build to mostly-statically-compiled binaries? (With the exception of a link to libc.) (This isn't a rhetorical question, this is something I don't know a lot about
I'd imagine the biggest cultural reason is that many Rust developers were C developers who had a reason to find something better, but still scoff at garbage collection, large runtimes, etc. They probably have a lot more Rust expertise in their circle.
Another technical reason is that they were trying to replace their C code with Rust in bits and pieces before they went with a full rewrite. I don't know about Go, but this is something ergonomically doable in Rust.
Rust can create statically-compiled binaries on Linux by using musl instead of glibc, but it’s not the default like it is in Go and is as a result not quite as effortless. There are a lot of crates with native dependencies that require slight environment tweaks to work on a musl build. Go on the other hand goes to great lengths to not need to link to any C code at all, to the point of shipping its own default TLS library and cryptographic primitives.
Plus, Rust has a more expressive type system.
I like loose type systems for some quick scripting, but I started to adopt Rust for many of my personal projects because I find it's so much easier to get back into a project after a year when there are good type system guard rails.