I didn't look closely into either flatpak nor appimage. But I get the advantages of such a system and I think it might actually help with the "Linux on the desktop situation". It's very easy to deploy something with restricted access to the file system, something that has all its dependencies in one place, that updates atomically, etc. It's also nice for random app vendors to be able to know that all their users are on the latest version, or not far behind. Could even push some devs to consider going back to desktop apps, as opposed to the web, knowing that they wouldn't have to deal with 1234 different, obsolete versions because someone's grandma didn't update her system in years.
After spending some time reading the exchanges on the posted link, I've come to the conclusion that the actual problem with snaps might not be snapd nor the automatic updating in and of themselves.
Rather, the problem seems to be a scope mismatch. This whole snap thing looks to me as something that should be aimed squarely at the "desktop user". I use that term as opposed to "system use". So distributing Spotify or whatever via snaps? Great! LXD for a home user to test? Sure! But as a way of managing low-level system components on production boxes? No way!
So I have to say I don't necessarily take an issue with Ubuntu pushing this on the desktop version. Sure, it is a pain by certain aspects, main one being slow startup for apps. But pushing this on Ubuntu Core in its actual state is, to me, the real issue. Sure, apparently you can run your own "Snap Proxy" or whatever they call it, which allows you to manually approve upgrades, etc. But why go through this trouble? It seems easier to just run apt-get from a central location when you want and for the packages and versions that you want.