####For an in the wild example, Steam Deck.
Steam Deck runs Steam OS, which is a heavily customized version of Arch Linux by Valve. But unlike normal Arch installs, Valve has locked the System partition(/) to read-only.
The reasons they've done this is two fold. First, there's actually two copies of the system partition. The reason for this is that when an update is downloaded it's actually written to the other partition, not the one you're currently using. This way the update happens in the background, and then you just need to reboot for it to switch partitions and do some house cleaning. What this means though, is that any changes you might've normally made to the system partition, disappear, as they are now on the other partition you aren't using. So if any changes you make won't matter, not much point in letting people make them in the first place. Using Flatpaks, any applications users install would instead be stored in the user partition, and never touch the OS itself.
The second major reason for doing this, is consistency. If people are discouraged or blocked from modifying the system partition, then any bugs or issues that crop up are, 99% of the time, Valve's fault. And because of that, Valve can more easily diagnose and try to reproduce any reported issues, because theoretically, the user's Steam Deck should be configured exactly the same as one at Valve HQ. All that's needed is for a user to report what they were doing when they encountered the issue, and Valve can follow those same steps and hopefully encounter the same issue, get detailed logs, and hopefully quickly push out a patch as needed.
And that's one version of Immutability. Valve doesn't go the full nine-yards here, just enough for their use case. In other Immutable Distros, versioning is taken even further, where you can control multiple versions and reset the OS state on the fly as needed, keeping any changes to a minimum and in controlled sand boxes. There's a ton of use cases for these, but the most obvious benefits are for enterprise and mass-market solutions, where a single configuration is multiplied across a large amount of servers, or end-user devices, allowing for easier diagnoses of issues and pushing of patches. For end-user clients especially, if they aren't expected to be customizing the OS to begin with, it makes support much easier for IT.
For your average Linux user, the benefits aren't as large, as you'll often want to be able to tweak things to your liking. But your Average Joe that just wants a computer that can surf the web and install some apps that can be found as Flatpaks, an immutable OS that they can't easily screw up is a plus.