In the case of an engine failure / shut-down I don't think I would have a problem putting out a Mayday
It is called Crying Wolf. Sending out a Mayday for an engine shut down immediately denigrates the original true purpose of the call which is to advise all those listening on the frequency in use that the aircraft is in imminent danger of crashing/ditching and help is needed. Clearly the aircraft was not in a Mayday situation. A PAN call is quite sufficient unless you are a drama queen.