In fact, a lot of systems don't have a stable kernel interface, Linux is the exceptions here. In Microsoft Windows, one must link against Kernel32.dll to communicate with the kernel. On OpenBSD, the libc provides the stable syscall interface (and in fact the kernel will refuse syscalls from outside the libc as a security measure, see [0]). MacOS and Solaris are two other OSes where, if I understand correctly, syscall ABI is not guaranteed and must go through a common library. Go used to embed syscalls, and ran into a lot of problems because of this.
[0]: https://marc.info/?l=openbsd-tech&m=157488907117170&w=2
On the other hand, the structures required to do syscalls via libc/kernel32 are generally simple enough that it's not a huge deal, and the difference between doing a raw syscall and doing a function call is unlikely to actually matter.
Fun fact/pet peeve: on android, if you want to communicate with most services, you need to go through Binder. While the low-level Binder ABI is stable, the services written on top of it aren't, and often change in backwards-incompatible ways. This includes core services like SurfaceFlinger (necessary to draw on the screen). This means that it's generally impossible to create purely native software on android - you always have to call into Java to talk to those services.
I think some systems don't have a stable kernel interface. The system-provided libc is that interface.
On Linux I believe that this is possible (and fairly common using the MUSL libc), but that glibc doesn't support static linking and many people want to use glibc for performance and compatibility reasons.