iOS almost allows this for geo-location nowadays, where one can pick whether to give ones exact position or a much less exact position, and for photos where one can select exactly what photos the app should get access to.
Also, a question to security experts: In many apps say we want a UX where the user would immediately be able to see their recent pics and select from them (think recent photos bar in whatsapp), but app shouldn't be able to access them. Is it safe if OS provides it as a screen overlay service which doesn't require a separate screen/window, but runs out of process (a la file picker).
I have never seen it used in a real app. Most apps request permission to your entire address book.