Has anyone tried building a Linux distro that doesn't rely on a Unix-style shell? At least not as a core system component that's required for startup, package management and such.

Call it "Shellack Linux" or something

Jokes aside, I would genuinely be interested in seeing how realistic this is. I'm always disappointed that even though "the shell" is one of the jankiest languages out there, it's a load-bearing component of every Freeā„¢ OS, and that many people even consider this an actively good thing!
To be clear, I have nothing against scripting languages, even when used for core parts of the OS! I just wish that the world chose a scripting language that's somewhat adequate at its job. Maybe with some fancy features like detecting errors and not breaking arguments by default.