As of my understanding, immutable systems are useful for Devices that are more bound to change, like a Desktop...I do not see much benefit here for a stable server system.

This logic is kind of backwards, or rather incomplete. Immutable typically means that the core system doesn't change outside of upgrades. I would prioritize putting an immutable OS on a server over a desktop if I was forced to pick one or the other (nothing wrong with immutable on both), simply because I don't want the server OS to change outside of very controlled and specific circumstances. An immutable server OS helps ensure that stability you speak of, not to mention it can thwart some malware. The consequences of losing a server is typically higher than losing a desktop, hence me prioritizing the server.

In a perfect world, you're right, the server remains stable and doesn't need immutablitiy...but then so does the desktop.