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.
Flatpak does try to account for storage size by using shared base images. The main problem is that some Flatpak apps don't update to the latest base, and some use different base images altogether, meaning most of the time it needs to have several bases anyway.