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.
If people want the Linux desktop to become more ubiquitous in homes, it better damn well be the next evolution. Someone’s grandmother isn’t going to get on the command line when apt inevitably decides to break.
The concept is not new, and Apple has had .app containers for a very long time that almost always just works. So clearly the concept has long been proven.
Perhaps flatpak, snap, appimage aren’t the final forms of this concept on Linux, but it’s a step toward making application packaging and distribution much more friendly for the common masses.