Those team didn't became multi cup team with their miss with some high pick, but with the amount of good picks done in a short period of time. That's the key. Every team can and will select a real good player here and there, but if you draft one every 5 years you'll never go anywhere.
Chicago built there team from the 2002 draft to the 2007 draft. In those 6 years they form an awesome core of player: Duncan Keith, James Wiesnewski, Brent Seabrook, Cory Crawford, Dustin Byfuglien, Niklas Hjalmarsson, Jonathan Toews, Patrick Kane, Troy Brower ... and some guys who had their moments, Bryan Bickel, Dave Bolland. That's a really solid base to build arround.
Los Angeles dit it from 2003 to 2008: Brown, Quick, Doughty, Simmonds, Martinez, Voynov, Kopitar. A little bit less impressive than Chicago but still damn good and a beautiful base to a contender.
Pittsburgh struck gold with Crosby and Malkin for sure, so they are not a model someone should try to recreate, it's like hoping to draft McDavid and Mattews ... Still they add Letang, Fleury, Orpik, Muzzin, Goligoski, Staal ... so again a good core for a team.
Boston was the same. From 2003 to 2006, an extremly short span of time. Bruiins drafted Bergeron, Krejci, Kessel, Lucic, Marchand, Versteeg and some contributor like Stuart, Hunwick, Tompson, Sobotka. Bruins were a Cup contender for 6 years (and it could have been more) because of that 4 year span at the draft.
It's harder to do that when you don't have "gimmies" with high pick, but it's still doable, alot of name on those list are not top 15 picks. Boston might get a really good base with the draft from 2014 to 2016 with a little luck. Allready counting on Carlo, Pastrnak and McAvoy, hoping to add 3-4 other name to the list.