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.
I call a spade a spade. If you can’t handle two binary compatible versions of BSD being called distros just because it’s a Linux term even though by every possible definition of that term that doesn’t include the word “Linux” they absolutely are distros, that’s your problem.