Why not containerise everything? You need libreoffice? No problem, here is a docker or podman container.
Flatpak is basically GUI-optimized containers. It uses the same technology (namespaces) as docker and podman, just with some extra tools to make GUI-related things work properly. That’s why flatpak apps don’t use the system’s gtk version – they’re running in a sandbox with a different rootfs. You can spawn a shell into the sandbox of a specific app with flatpak run --command=sh com.yourapp.YourApp
and poke around it if you want to.
The thing with appimages is that they expect the developer to have full knowledge of what libraries need to be bundled with their app, which makes it difficult to make truly universal appimages. In flatpak you just select one of a set list of runtimes and add any additional dependencies on top of it. Flatpak also re-uses the files for each runtime in between the different apps that use it, which saves a lot of disk space.