I felt like after all these years I should finally contribute something, so here goes.
I wanted to look more into this: "and I think it's something like 2 or 3 teams in the last 20 or 25 years have won the cup without a 1st overall. Those are terrible odds. "
For each Stanley Cup winner, starting from 1980 NYI Cup Win:
# of times the winning team did not have a #1 Draft Pick: 25
# of times the winning team had their #1 Draft Pick: 17
# of times the winning team had someone else's #1 Draft Pick: 2
(although this actually excludes Gretzky, coming from the WHA and not a #1 draft pick)
Keeping more recent, starting from 2000 NJD Cup Win:
# of times the winning team did not have a #1 Draft Pick: 12
# of times the winning team had their #1 Draft Pick: 10
# of times the winning team had someone else's #1 Draft Pick: 1
So really this is about 55/45 in favor of not having a #1 pick on your team in order to win a cup
Going deeper:
The recent (from 2000 NJD) wins are from these picks: Vincent Lecavlier, Fleury & Crosby, Patrick Kane, Alex Ovechkin, Steven Stamkos, Erik Johnson
That's it. Of these, let's say Patrick Kane, Crosby&Fluery (on the same team no less), and Ovechkin could be considered "Generational Talent". They account for 7 Cups of the last 24. That's definitely sizeable, sure.
But that also leaves only three "very good, but not generationally good" #1 picks that won a cup in the last 24 years: Lecavalier, Stamkos, and Erik Johnson (and he wasn't even drafted by the 2022 Colorado team).
Another way to look at this, how many #1 Draft picks have won a Stanley Cup?
Going back to 1980, of the 44 #1 draft picks, only 11 of them won a cup, and 2 of them were with a team that didn't draft them. That's only 25%.
Make of that what you will, but personally, tanking for tanking's sake is not a winning strategy. It did work for Pittsburgh (twice actually, which f***ing pains me), but it's failed way more than succeeded.