I am curious about your situation that causes you to edit files remotely. I've never had to edit files anywhere but my local file system. Are you developing or is it more of a devops/sysadmin kind of role?
To give you an example of what you can do I often use tramp locally to edit files as root: instead of having to fire a different instance of an editor as root to edit a config file I can just do it "remotely" from my main Emacs instance, with all my config and without worrying about messing something up by having the entire editor running privileged.
I work in embedded development so I also often use it to browse and edit files on the live target system (beats using a crappy dumbed down vi from busybox). And of course as you mention for general sysadmin tasks it's also great, I'm a developer but that doesn't mean that I don't have some sysadmin to do from time to time.
My current solution is just SSH/Vim but I think I'd like to go back to a graphical editor. I like Vim but sometimes it's a hassle on the big projects.