I don’t understand what problem they are meant to solve. If you have a FOSS piece of software, you can install it via the package manager. Or the store, which is just a frontend for the package manager. I see that they are distribution-independent, but the distro maintainers likely already know what’s compatible and what your system needs to install the software. You enjoy that benefit only through the package manager.
If your distro ships broken software because of dependency problems, you don’t need a tool like Flatpak, you need a new distro.
simple example: the app that you want is outdated, is missconfigured on the distro’s package manager (e.g. OBS on arch missing wayland capture). If this app has a flatpak version, it’s likely it’s mainained by the same people who makes the app, thus they can make sure it works fine through flatpak, and since it’s distro independant it works everywhere. App images just bring all their dependencies with them, and snaps idk never used them…