Obie
Quite! In 30 something years and with a good share of unusual circumstances, I don`t recall anyone using "mayday" and only one "pan" call. If there was any doubt, one only had to say something like "roger, do you wish to declare an emergency?" This always resolved any doubt and gave justification for some unconventional actions. I can only think of one occasion (where I was a bystander) where insufficient information was given on the first call, quickly resolved by that phraseology.
In the case of the Hudson river episode. The pilot made an exemplary call...
1 What happened .....he`d hit birds
2 Consequences....he`s now flying a heavy glider
3 Intentions....trying to return.
I really don`t see how that call would have been improved by adherence to an "ideal" phraseology. However, I agree there are occasions when this might be a good thing to do.