You ever heard of a good, solid tank?
Every single Cup champ for the last 13 years has had major pieces taken high in the draft.
Well first of all this just isn't really accurate. Bruins in 2010 had Seguin sure, but it was his rookie year and he only played about half the playoffs and didn't make much impact. Nathan Horton was a high pick but he was injured. Boston never rebuilt, they had two off years, where they went from being 4th in the league, to missing the playoffs for two years, but then were back in the year afterwards, then 2nd in the league the year after that. Then two years down the road they won the cup.
St.Louis just won the cup and they're only high draft pick was Pietroangelo at 4th overall. They didn't tank to become successful unless you consider getting the #1 pick and taking Erik Johnson in 2006 influential on their cup run. They also hadn't had a draft pick in the top 20 of the draft since 2010.
Second, basic distribution results in every team having an array of high first rounders. There's 20+ players per team and 31 teams in the league, it just makes sense that each team will. So claiming a correlation between teams winning the cup and having high picks is fairly fictitious logic, because you could see the same trend with teams doing poorly. And to prove it, here are the stand out top 5 picks from each team:
Colorado – MacKinnon, Landeskog, Makar
Vegas – Pietroangelo, Fleury
Arizona – Strome, Kessel
Los Angeles – Doughty
San Jose – Marleau
Carolina – Svechikov
Florida – Ekblad, Barkov, Huberdeau
Tampa Bay – Hedman, Stamkos
Nashville – Johansen
Dallas – Heiskanen, Seguin
Chicago – Kane, Toews, Dach
Detroit – Ryan, Raymond
Columbus – Jones, Laine
Washington – Ovechkin, Backstrom
Pittsburgh – Crosby, Malkin
Boston – Hall
NY Rangers – LaFreniere, Kakko
New Jersey – Hischier, Hughes
Philadelphia – Patrick, van Riemsdyk
NY Islanders – Dal Colle
Buffalo – Dahlin, Eichel
Ottawa – Tkachuk
Vancouver - Pettersson
Montreal – Price
Toronto – Matthews, Tavares, Marner
Edmonton – McDavid, Draisaitl
Winnipeg – Wheeler, Duboius
Calgary - Lindholm
The only teams without a top 5 are indeed Minnesota (althoug Koivu was 6th overall and just retired), St.Louis (who just won a cup, and recently lost Pietro), and Anaheim who has a 6th overall (Lindholm).