Regular season defense is not equivalent to playoff defense. Regular season hockey is a track meet, playoff hockey is Iowa football: much grittier, physical, defensive, guys actually care.
You can win the Avalanche/Penguins way with less physicality, but only if you dominate puck possession, have great depth scoring, and above average goaltending, plus your elite stars. Teams like the Blackhawks, Lightning, and old school Red Wings had elite players and depth players who played with a bite/edge. The Kings, 2023 Golden Knights, 2011 Bruins, 2019 Blues honestly didn't have that many elite players, but they had guys who were willing to play with football mentality, play actual defense, timely scoring, and good to very good goaltending.
But yes, Cooper is stubborn.