I used to think like that, Flatpak as a solution to Linux packaging and all, but it felt short when I installed the wireshark's flatpak and tried to make it work, there was a bunch of permission errors and all. Because I was using Fedora Silverblue at that time, there was some recommendation to use toolbox instead (which is based on podman) and then I asked myself if it's even necessary? Imho your frustrations are better addressed by NixOS, not some combination of Docker and Flatpak. Don't get me wrong, Flatpak is great, but you can't rely entirely on it.
True, there are still exceptions that don't work well with Docker and Flatpak.