West Coast :
Nobody ( I think) is suggesting than faced with an Emergency descent you should first contact ATC and request ATC instructions !
What I ,and others here ,are saying is that, in order to be the safest ( which we all strive for )when faced with an emergency descent , call Maday and turn 7700 as soon as you can. No pan-Pan, no long stories, and not wait until things are over.
Yes, the big blue sky works most of the time , but in a complex and congested airspace luck will run out one day.
So why not increase your chances to have a fee path below to descent into ?
We pilots and controllers are normally very good at multitasking. (The women among us even better
) Why not ,WHILE AVIATING , pressing the PTT and saying something like : Company (*) Mayday-Mayday Emergency descent "
Training for this in the Sim , so that it becomes a reflex will help.
Then training controllers how to reply in a consistant manner ( i.e everybody everywhere knows how to react) will also help.
(*) experience shows that in many emergencies pilots under stress get the trip number wrong. not an issue if pilot( or someone else in the cockpit) squawk 7700 )