There are already non-GNU alternatives for these utilities with non-copyleft licenses. BSD use them.
GNU utilities will remain in C and licensed under the GPL. There is a competing project called uutils with the goal of re-writing clones in Rust. That project also happen to use the MIT license. But this project may fail or succeed (even if it works, it doesn't mean people are going to ditch the GNU utilities). But what matter is that this is a competing project.
The Linux kernel doesn't have a direct competitor using Rust as a programming language. Rust is being used inside the Linux kernel project for some new code/refactors. And that code is still GPLv2. So I don't see why you bring a uutils analogy. There is nothing in common.