I am under the impression that no-std code is primarily the concern of embedded systems that might not have much of an OS [1] at all, nevermind a suite of system calls to Linux.
[1] Like a typical RTOS, that may provide some basic communication primitives, thread creation, and a hardware abstraction layer (HAL).
That is nor necessarily the case. Embedded is a big user, but there are other reasons to use no_std, such as explicitly wanting to avoid heap allocations, or wanting greater control over the native APIs being called.
Also Wasm support (can be viewed as a kind of embedded) and better portability. Anything that helps one separate the platform and more precisely define the platform boundary the better.
Libc is necessary, but not good.
In any case, I hope it remains separate. Third-party no_std code would benefit from it.