I’m pretty sure ATC’s job is to figure all that stuff out…. It’s why you are there in the first place. A Mayday/Pan is obviously useful but I’ll stick to flying the aircraft/avoiding terrain over chatting with someone on the ground who can’t do anything to help in the initial seconds/minutes.
Your job in that rare scenario is to get everyone out of our way and to REDUCE our workload. I hear so many scenarios in the US when ATC only complicates the problem and refuses to listen to the words that are being spoken. It’s sort of embarrassing/shameful for people who are supposed to be “professionals”.
And don’t get me started on French/Spanish atc….