The kernel doesn't have to support POSIX. You can do the emulation in user space. The only tricky part of POSIX is fork, but chances are you won't need that for compilers etc, just exec.

In any event don't confuse the journey (some POSIX compatibility in order to advantage of existing toolchains while building your new OS) for the destination (clean, elegant, new API, world changing, nifty) OS.

And if you are going to have command line tools in your OS, they will need an API and you may as well pick a useful subset of POSIX.