Good coaches coach according to the roster they have. Trotz certainly leans defensive, but I think he coaches with what he has. Those Islander teams were not talented enough to win by running-and-gunning, so he went heavily defensive with them. And it got them pretty f***ing far. When he had a highly skilled Capitals team, they finished 6th, 2nd, 3rd, and 9th in GF. So it's not like he wants to win 2-1, but if that's what it takes, then that's what he does.
Losing 6-5 is better than losing 2-1, but sports are fun to watch when there is something on the line. If winning 2-1 is what is needed to win, then sign me up. No idea if Trotz would take the job, but if he would, I'd welcome him with open arms.