Wow, I had the same thing on my mind. After submitting this post, I was thinking that it would also be nice if we could do special backups for our sites, keeping the Webinoly settings (ssh, cache, httpauth users etc) and then just import them with a single command - I was planning to submit a new feature suggestion for that :D.
This could have even more value if you had the option to also do it for the entire server, as you suggested, or even for multiple specific sites all in one command (e.g. backup a live site and it's staging).
As for the migration part, being able to move them between servers via SSH would be really convenient. From time to time I have to move one or more sites to a new server and it can be relatively time-consuming. I believe that other people might have the same need too.