You already have a de facto GNU OS at the moment in the form of the Guix System Distribution (GuixSD), what with it letting you configure the entire system in Scheme, perform transactional upgrades, system state rollbacks, it has its own init daemon and service scripts in Scheme, etc.
At the same time, we've been seeing some efforts in creating tiny builds of the Linux kernel [1] that go as far as to reduce syscalls, VMM algorithms, capabilities, character devices and so forth. There's also the recent Linux libOS effort to create a network stack in userspace as a shared library, though that seems about the extent of it. NetBSD then gives you a userland driver framework with rump kernels.
So what one can do is build a really stripped down Linux kernel, write a Mach IPC compatibility layer, run the Hurd servers on top of it and plug in the resulting product with GuixSD. And you now have the complete GNU system. As far as you'll ever get, anyway.
This has already been discussed before [2], but it's not something that has ever been given any priority. With the current climate, it might be worth a shot.
As to why anyone would want to do this... well, for one you get a full OS that is entirely configurable in Scheme with all of its services running as userland file servers (translators) in a sort of Plan 9-ish way, all the while supporting the Linux API. That's still pretty ahead of GNU/Linux. The Hurd also has features like running multiple instances of itself in user mode (subhurds) that can serve a similar purpose to containers.
It's obvious no one's going to port the Hurd servers away from GNU Mach, so this is the best shot anyone has. Any Hurd or Guix devs in here to comment on this?
[1] https://tiny.wiki.kernel.org/
[2] https://www.gnu.org/software/hurd/open_issues/linux_as_the_k...