I know AppImage was though to be OS agnostic, and make an OS for it sounds a bit contradictory, but the idea is not about an “end-user” OS; rather a faux OS to use as AppImage generator.
As for base can be used a very barebone *buntu derivative (let’s say, about a live iso of about 300MB) to be used as development kit.
All the library and dependences installed by default are listed in a special register: those basic libraries (let’s call them foundation libraries) are never stored in the app image as we presume that any functioning Linux OS already has them working.
Anything installed duiring OS runtime will discarded later: each time the OS boot it always return to a neutral state so a an AppImage autogenerator script is always in default situation; an less unpredictable configuration/setting can interfere with AppImage generator.
This ISO could even run into Qemu (so, maybe have it AppImag-ed as well? AppImage while you AppImage Inception?)
It may be even theoretically possible to have specialized AppImage iso that bundle together special software with other packages (ie: emulators, wine or even full sdk toolset).
The method can be something like this:
a special script like appapt does something like:
apt update then
apt installthe required package with all dependencies (which are stored in a special list)
Once downloaded and installed, user is then shown a list freshly created icons in the /usr/share/applications folder (only the new ones, old icons already there are ignored).
Once picked one, the script proceed into package all the required dependences and set up binary name and icon based upon the user’s previous choice.
Unfortunately I don’t have the scripting/OS maintain skills to actually make it by myself; it’s just one idea for the community. Maybe this Ubuntu 18.04 derivative could be a starting point? (~260MB of bootable ISO, can be further reduced by removing apps)