Being able to run some applications from super fast but small NVMe disk and less important ones from slow but huge spinning rust disk, being able to run applications from a network share, CD, USB stick, etc. Desktop OSs have been able to do these sorts of things since the 1980s without all the hoops Linux Desktop software makes you jump through to do them.
> Being able to install and run flatpaks from any directory seems like it’d be difficult to implement for little benefit.
If Flatpak had considered this ability from the beginning it wouldn't be. Hell it might not be that difficult now, I haven't looked at the source for Flatpak and how it does things behind the scenes is otherwise not documented as far as I can tell. As you mentioned, AppImage implements it without much difficulty, and AppImages can be securely isolated by firejail. Combining the two concepts in the same package shouldn't be that hard. Keep runtimes in "installations" and let applications exists as single-directory self-contained units wherever the user wants them. What is fundamentally difficult about this?
> unnecessary since AppImage already offers exactly that functionality
If AppImage were fast becoming the new standard in Linux Desktop application distribution we wouldn't be having this conversation.