> What I mean is that there are init systems that only require POSIX compliant APIs

Those are irrelevant as they can't even do basic tasks like shutting down the computer or restarting it. Feel free to find a POSIX API for Linux' reboot syscall.

Some systems also require mounting additional filesystems, again not possible in a world limited to POSIX interfaces.

Sandboxing, SELinux, ...? Not in POSIX.

And so on.