So root still has write access to the system then

No, not while the system is running. The base-layer of the OS is fully read-only.

An update doesn’t write to the existing system, it creates a new one that will be switched to on next reboot. So the current system is not actually changed, hence the term immutability. This has two benefits:

• atomic updates: either the upgrade is successful and you switch over to the new system, or it isn’t and you stay on the untouched current system. There’s no way to end up in a broken OS because an upgrade went sideways.
• rollback: the old version stays untouched on disk, so even if the upgrade was successful but something still turns out to be broken after you boot into it, you can just switch back to the old, known-working system