From the limited experience I had with an AppImage I found they usually create a .desktop file to make the program searchable. Though I have to agree that there is no really simple, gui way to install AppImages.
Yeah mine used to in 18.04 and now they don't in 20.04. No release notes about the removal of that feature, no workarounds, nothing. Not that it's a big issue for me to create a .desktop file myself but the apt-get experience is slightly nicer still because everything just works.