This is incorrect. The syscall ABI is the supported stable ABI for Linux, not the libc API - there's no single supported C library for Linux, and libc often lags behind the kernel in terms of providing syscall wrappers, so punting it to that level wouldn't work. This is in contrast to the BSDs that have libc tightly coupled to the kernel.

Of course, the Linux solution results in some weirdness, especially because specs like POSIX cover the C API, not the syscall ABI. setuid() at the libc layer is specced as changing the UID for all threads in a process. The Linux setuid() syscall only changes the current thread[1], and it's up to the C library to do some absolute magic to then propagate that to all other threads. Which made things difficult for things not using the C library, like Go (https://github.com/golang/go/issues/1435). But that's still not an argument that the supported interface is the C library - the kernel advertises the interface it exposes via the syscall ABI, and will retain that functionality, and if you want POSIX compatibility then you get it from somewhere else.

[1] In Linux, a thread is just a very slightly special case of a process