Yzerman was the only early first round pick on those teams. Everyone else that made up the core of those teams was a late round pick. Lidstrom, Fedorov, Konstantinov, Kozlov etc were all players that any other team could have had. Either that or they came over through a trade (Shanahan, Larionov, Larry Murphy).
It took a long time to transition from the "Dead Things" era to when they won and competed for Cups, kind of similar to what the Capitals went through.
Take a look at all the players they got in the Yzerman draft. Something like 5 regulars from that team. That draft turned the tide.
I'm not saying that the Red Wings weren't a special team or that they did something wrong, I am saying that the claim that the Wings didn't suck their way to being a top team isn't really correct. They sucked, they got Yzerman and a bunch of other players that turned them in the right direction and then they were able to draft extremely well and make good trades and signings and win cups.
The Wings were one of the worst teams for a very long time, the Oilers are getting to the level the wings were at. They have to have another few years of being a bad team to be on that level.
Most teams win championships by drafting well, making trades that benefit their team, and signing the right players just like the Red Wings did, the Red Wings just managed to stay decent longer than almost anyone else ever has. That is a great accomplishment but they still sucked their way to drafting Yzerman and he was the key for those earlier teams.