It really feels like apps should be required by App Store policy to separate out their notifications into "delivery channels": at least, one channel for urgent/timely notifications, and a separate channel for "something has changed, no need to check right now" notifications. Where users should then be able to configure the notification policies on each of an app's delivery channels separately.

Then, every type of notification an app can send (i.e. every string-template for a notification message) could be required to be pre-classified with the delivery channel it will use at app version release time — with the App Store review team rejecting app updates if the update, in their opinion, misclassifies the "proper" delivery channel for a given message-template.