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.
Just a shot in the dark, but it sounds like you have never maintained software. If you have, then my apologies, but your experience must not have included much by way of dependency and version management. Dependencies and versions are a major source of headache for any software engineer and it’s a problem of our own making.
Having completely self-contained applications, while more bloated, makes maintenance and distribution exceedingly simpler and puts the burden of managing that solely on the developer of said application instead of burdening everyone down the line.
I remember when package managers didn’t exist. It was painful. This is the next step in the evolution of the Linux desktop that was mostly solved in Windows and effectively completely solved on macOS since some early 10.x version.