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.
One thing I like about about Flatpak in particular is it allows me to have newer applications on distributions with older package bases (for instance, Debian.) I don't much care for rolling release distros, and I'm not a fan of having to hunt for a 3rd-party repository, so for that purpose I really love the option to just get a Flatpak.
Also Bottles. Bottles is great.