Originally Posted by
Auxtank
Absolutely this.
"We've got this sh1t we're dealing with and we're in YOUR Airspace."
Agree. And there's one other thing. Almost everybody monitors 121.5. So if you put out a call on 121.5, everybody will be listening and first try to figure out from your position report whether you're in their airspace or not. By addressing the ATC unit specifically everybody is able to skip that step.
OTOH if these subtleties are lost on you while dealing with the emergency, don't worry. You've got other things on your mind. Aviate, Navigate, Communicate. And for most emergencies there's not a lot that ATC can do about them anyway, other than clearing the skies and the runway for you. Squawk 7700 will achieve that just as easily.