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 libraries do have versioning. So the system can sort that out… maybe. You also do not want the same app indirectly loading multiple versions of the same library. You do kind of want to have all apps on your system linking to the same shared image though. If it does the system needs to only have one in memory even if multiple running apps are using it. This is a big space and load time savings. These separate binary formats though handy have their issues.