Alternative libc implementations just aren't a thing outside of Linux. However, if, for some reason, you really want to re-implement libc, you still can, but y

Alternative libc implementations just aren't a thing outside of Linux. However, if, for some reason, you really want to re-implement libc, you still can, but your library will have to link against the system-provided libc for the syscall entry points, because that's the only stable interface to the kernel. There's no reason that should be a problem for a hypothetical libc-reimplementor.