I find it hard to imagine a system that is not borkable by a superuser. Maybe it’s helpful to think of immutable setups as harder to bork by accident during routine maintenance (e.g. through faulty updates) and more resilient to bad code (through containerization).
You’re right that “immutable” is a bit of a misnomer in that regard, and it’s been argued that “atomic” is a more fitting term.
And I agree that a lot of documentation and how-to-guides don’t account for immutable setups (yet?), which can get novice users especially in a lot of trouble.
Personally, I prefer a declarative system (NixOS) that solves this problem rather cleanly and gives me most benefits of so-called immutable distros as well.