I wonder if this couldn't be solved at the OS level. Maybe there could be some kind of a flag that, if the OS sees it, the app is not allowed to store/save/communicate/whatever. Then, any app that has this flag doesn't need a privacy policy because it is OS restricted from doing anything that might require such a policy?

I suggest this as someone who has no experience whatsoever in making apps or mobile operating systems (beyond being a user of one), so I don't know how practical it is.