And for writing kernels the same applies; without the stdlib, it gets a lot smaller very fast. I've done it, so I think I can count myself on having some experience there. The biggest part of my kernel is a 128KB scratch space variable it uses during boot as temporary memory until it has read the memory mappings from the firmware and bootstrapped memory management on a basic level. The remainder of the kernel (minus initramfs) is then about 1MB large, the largest part after the 128KB scratch space using about 96KB.
FWIW, this is does not seem to be empirically true. The savings are possible in theory, but false in practice.
https://drewdevault.com/dynlib.html
The most used largest libraries, like libc and libpthread, would be dynamically linked by Rust anyways.
In a larger sense, something that sets out to be a "systems programming language" needs to be exactly the sort of thing suitable for a tiny embedded system, even if it isn't running on one, because everything else builds on top of it. The attitude that "we have tons of power, why not waste it" just doesn't fly at the very lowest levels. You can write a desktop application in Python, and it's broadly fine - but try writing an OS kernel!