Compressor Stall.
In my first post I mentioned the take-off alternate was required if the departure airport was closed to arrivals. Fair enough regarding Oz. I've not worked there for some time. It was the general principle of a take-off alternate, Australia excluded.
In the last post I apologise for my lack of clarity. I said "Of course with 2 engines operating, and engine failure probabilities being low, we would most probably keep going if time intervals were reasonably insignificant". I meant being already inside the ETOPS threshold for the airport that became unavailable.
With regard to your last point, you may well be correct. ETOPS defines the total area of operation. One may well be able to choose one's preferred airport. But I wouldn't wish to expose my PAX and aircraft to the additional flight time on one engine in case something were to happen to the other one. That's where the probability and risk enter. I'd possibly be facing severe penalty if my judgement was wrong.
Certainly food for thought.