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.
Another kind of silly benefit is that distros without their own graphical package manager can use the gnome one with Flathub. I actually started installing NixOS on my family’s computers, because I can start from a common config and have everything up and running quickly. Plus it’s super stable. And with Flatpak, they can install software after I’m gone without editing the config. It’s kinda like my config is the base system, and then they can layer on top.