<<An engine failure may, or may not, be an emergency. It's not wrong to call Mayday, and it's not wrong not to. It depends on the situation. Your call, and you get paid to make that decision>>
Exactly...
In fact, in the above thread, it is NOT the Engine Failure that warrants the Mayday. It is the immediate, unavoidable descent (if required). As was pointed out, Mayday implies "immediate assistance required", and ATC are unable to assist with the failed engine! They are however, able to immediately assist with the descent, and in slower time (hence maybe downgrade to PAN), with the diversion...
NoD