I managed a CentOS system where someone accidentally deleted everything from /usr, so no lib64, and no bin. I didn’t have a way to get proper files at the time, so I hooked the drive up to my Arch system, made sure glibc matched, and copied yum and other tools from Arch.
Booted the system, reinstalled a whole lot of yum packages, and… the thing still worked.
That’s almost equivalent to a reinstall, though. As a broke college student, I had a laptop with a loose drive, that would fall out very easily. I set it up to load a few crucial things into a ramdisk at boot, so that I could browse the web and take notes even if the drive was disconnected, and it would still load images and things. I could pull the cover off and push the drive back in place to save files, but doing that every time I had class got really tiring, so I wanted it to run a little like a live system.
An immutable OS is useful for things like an alarm clock, where if you accidentally muted the sound system, you could oversleep. There’s an obvious downside if you’re someone that watches porn on your alarm clock computer, but sometimes compromises must be made.