Boxes is an application, not a system service. The two are completely different.
Flatpak is for applications: things that run with low privileges, and contact other services. The Shell, system settings, and all the other parts of a desktop session are privileged components, and as such cannot be containerised or sandboxed.
GNOME is the desktop. It’s a desktop environment. That has nothing to do with whatever metaphor it does or does not implement.