I think its more of a one step at a time thing. There is nothing about the design of flatpak which prevents permission popups. The problem is that every desktop program must be rewritten to support this idea and most linux desktop app devs are only vaguely aware of flatpak, let alone ready to start designing specifically for it.
The current strategy seems to be having outsiders packaging all the desktop software in to flatpak while disabling any sandboxing that gets in the way. This brings you to the same state as traditional package managers with little security, but it boosts the flatpak ecosystem and makes it ready for the average person. At that point app devs will be more aware of it and can build their apps to tolerate missing access to things and prompting for access.
The current strategy seems to be having outsiders packaging all the desktop software in to flatpak while disabling any sandboxing that gets in the way. This brings you to the same state as traditional package managers with little security, but it boosts the flatpak ecosystem and makes it ready for the average person. At that point app devs will be more aware of it and can build their apps to tolerate missing access to things and prompting for access.