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.
It’s probably not of any benefit to you as a user if it’s also available in the package manager.
It helps you if you want something that’s not available in your distro, or a different or maybe multiple specific versions, or you want to contain some stuff and use the additional permissions system. But you don’t have support by the distro maintainers this way and it’s not tied into the rest of the system any more. I always use the packaged versions if available.
Other than that, software developers can use it to just do one build for their homepage that works on every distro.