Given that iOS manages everything else in the status bar, it's a mystery to me why each application is supposed to implement logic for displaying the network activity indicator.

Fortunately, AFNetworking will do it for you:

AFNetworkActivityIndicatorManager manages the state of the network activity indicator in the status bar. When enabled, it will listen for notifications indicating that a network request operation has started or finished, and start or stop animating the indicator accordingly. The number of active requests is incremented and decremented much like a stack or a semaphore, and the activity indicator will animate so long as that number is greater than zero.