Is the weakSelf/strongSelf dance really necessary when referencing self inside a non-retained completion called from a UIViewController?

As I believe you correctly diagnosed, using self will not necessarily cause strong reference cycle in this scenario. But this will retain the view controller while the network operation completes, and in this case (as in most cases), there’s no need to. Thus, it may not be necessary to do use weakSelf, but probably prudent to do so. It minimizes the chance of an accidental strong reference cycle and leads to more efficient use of memory (releasing the memory associated with the view controller as soon as that view controller is dismissed rather than unnecessarily retaining the view controller until after the network operation is complete).

There is no need for the strongSelf construct, though. You can:

- (void)makeAsyncNetworkCall
{
    __weak typeof(self) weakSelf = self;
    [self.networkService performAsyncNetworkCallWithCompletion:^{
        dispatch_async(dispatch_get_main_queue(), ^{
            [weakSelf.activityIndicatorView stopAnimating];
        });
    }];
}

You only need the weakSelf/strongSelf combination where it’s critical to have a strong reference (e.g., you’re dereferencing ivars) or if you need to worry about race conditions. That does not appear to be the case here.