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.
Linux is a bad attemot at copying UNIX. BSD comes from the orginal UNIX of the 70’s. BSD was a summary of the patches, fixes, and other developents that was applied to the Unix codebase and then after the lawsuit took the original UNIX patches and started BSD 4.4-lite