Example #1, since it's an "app" you can't remove but that many (I'd guess not far away from most?) people use, is Mail. I wish my email servers would send push notifications, but they don't, so Mail is constantly checking for updates. That uses battery, but it's something I want it using battery for. And then in battery saver mode, it stops automatically checking, so you won't notice any new emails until you either turn off the mode, or go into Mail and manually have it sync.