Delays of this nature can happen with any airline, and are perhaps more of an issue at remote locations (vs hubs where a/c could be more easily substituted if needed).

I don't think there are any official on-time stats in NZ, but in Australia DOTARS keeps some stats. Perhaps someone could look up EK's performance?

I sometimes see EK in AKL running an hour or two late, but normally reasonably on time. LA is the chronically late airline in recent weeks (many times AKL-SYD-AKL is cancelled to recover about 10 hours of the delay).

Buying insurance when you know your flight is delayed is almost certain to result in no cover for missed connection (a basic principle of insurance). You need to buy insurance before the trip starts.