And they aren't integrated in to the OS like snap or flatpak. I can install/update a flatpak and it shows up in the program menu. For appimage I have to open my filemanager and click on the program like a prehistoric windows user.

Also last time I read the OP article the tldr is "Flatpak has security options but many packages turn them off making them exactly as secure as appimage/binaries from a package manager"

The appimaged daemon automatically generates desktop entries for AppImages placed into a designated directory:

https://github.com/AppImage/appimaged

The main problem with AppImages is that there is no easy way to update them in bulk.

I think this is something that can eventually be fixed. Indeed, I'm on Linux Mint and the integration is actually pretty good. When you first run an appimage it asks if you'd like to add the program to the start menu. Icons are correct and everything.

I can also imagine some possible ways to allow appimages to auto update, though I suspect there'd be a lot of resistance to that.

I'm not really aware of a single way appimage would be better than flatpak. To get the integration and updating working you would need to install a tool and not having to install something for appimage is the only benefit I see over flatpak. It makes it easier to just quickly download and runs something but less convenient in the long run.

Also in the future I can see apps being built to actually use the permissions system in flatpak so it doesn't have to be disabled. Flatpak is a step forwards for linux where as appimage is restoring bad practices from windows.

I've been thinking about this, and please correct me if I'm wrong, but I think it's a good choice for certain classes of closed source apps. For example, I'm building a video game, and I'm going to distribute it through Steam. The Linux version is going to be an appimage to guarantee maximum compatibility. Flatpak and Snap make no sense in this context. Auto updates are handled through Steam, as is integration with your system like creating icons and what not.

Also, from the research I have done (which I'll admit is inadequate), the process of building an appimage seemed more straight forward than either flatpak or snap.

I'm not really sure how a flatpak in this case would be any better than just a binary of the game with all its libraries included. I'd like to see stream distributed as a flatpak with access cut off from the rest of the computer so malicious game drm can't scan through your files.