it would be interesting to hear the benefits and problems of
that approach.
A big problem is that libc interfaces are more stable, which means with libc you don't need to recompile as much when the system is upgraded, if ever.
Solaris and Linux work hard to keep their kernel interfaces stable, so it's less of an issue there. But Apple, for example, very explicitly says that kernel interfaces (Unix syscalls and Mach ports) are unstable and unsupported, generally speaking. Consumable interfaces are provided via the userland runtime (e.g. libc). Notably, Apple's toolchains don't even support static compilation.
A system like OpenBSD isn't so gratuitous as Apple in terms of breaking compatibility, but because they're focused on improving and simplifying a cohesive system, they don't flinch about breaking compatibility when needed. For various reasons that happens more often with kernel interfaces than with libc interfaces.