There's some work being done to dockerize the install. If that doesn't do the trick for you, I expect some of the same automation will.
Are there plans to have an easy way to update ones website, i.e. through pressing an update button, as opposed to having to do not-always-straightforward file manipulations on the server. If there's anything to draw from modern web applications, this is one of those things.
At this moment, for example, my board is 0.7.2, and my web developer is gone. You may have already implemented this in 8.1 but I wouldn't know, since I haven't a clue how to update... xD
We do offsite installations and upgrades, message firstname.lastname@example.org
Of course, we do have docs so you should try it yourself just back up everything first!
Edit: to answer your original question, we do plan on building an upgrade button into our hosting plans control panel - right now we just upgrade customers manually. It's probably impossible (or hard) to make an app upgrade itself via acp, we would need to make the acp a standalone application (we've toyed around the idea, but not worth the development time)