At training for a US carrier with ~300 widebody aircraft, it is insisted that we use Mayday or Pan Pan as appropriate, including upgrading or downgrading between the two or cancelling as appropriate (at least on our specific fleet type). The students do it well enough to get through training, although in most cases it has to be taught, even though the average trainee has been flying professionally 10+ years. As most of the newhires are around age 40 it is very difficult to drive out their previous bad habits. What they do in the real world when situations occur may well be a reversion to law of primacy coming from whatever they learned in the military, or a small local flight school. I can't explain why so many of my colleagues are non-chalant about R/T. Luckily CPDLC is taking over so maybe soon it will be a non-issue most of the time! When I started as an EMB-145 FO decades ago we were all just taught to say "declaring an emergency" and that was it, granted that airplane did not leave North America.