HIGH EXPECT
I disagree with your view that a two engine plane now on one engine, is just being a single engine plane.
A two engine plane that has lost one engine is a crippled aircraft and in an emergency situation.
Would you declare an emergency in a light single engine plane if the engine could only develop 50percent power?
The use of mayday vs pan is an odd question. I understand that in countries where multiple languages are used that standard radio phrases are important.
I can think of times that emergency should have been declared (using mayday). And that differences in language can make things even more confusing. I can think of a 707 inbound to KJFK that ran out of fuel after much trouble along the way. And ATC not really understanding how bad things had gotten.
The pan vs mayday question is one that is easily covered in the USA> I daresay most pilots would never use PANPAN. Its either an emergency or it isn't.