That's not what really happened though. Chicago won their Cup and was in immediate cap hell. They had to sell off and re-tool to build back up. Once they did, they won 2 Cups in 3 years. That middle year between Cups 2 and 3, they went for it... they just lost to LA in the WC finals. LA also won 2 Cups in 3 years while going for it each time. The year they lost was the year Chicago got their revenge in the WC finals. There really wasn't a one year on, one year off situation with those teams. They were runs that just ran into one of the other great teams of the era.
Avs are really not like those teams, especially early in their runs. Avs are more akin to the Caps in reality. A team that struggle to get out of the 2nd round, broke through in a great year with middle to late core.