And that's exactly how it works for apps you download from the App Store. Apple even makes app publishers declare data collection and privacy practices on the App Store before you install apps.
It's clearly just Apple not wanting to further open up their platform to competition.
Not only that but it's an honour system they aren't checking any of the privacy policies or labels for accuracy, just last year a whole bunch of high-profile apps like Candy Crush Saga and Clash of Clans got caught claiming suitability for all ages while their privacy policies banned under 13s so they could advertise and collect data indiscriminately.
They should be checking things like that. It's something that you'd expect to be covered by Apple's 30% cut.