Rebuilding in the NHL is actually fairly easy. It just takes a really long time, but patience is usually rewarded. The combo of the draft system/8-year max contract length/hard salary cap with no exceptions/hockey "culture" that places an emphasis on superstar players if nothing else giving an extended go at it in their drafted location and not behaving in a mercenary fashion basically sets things up in a way that the league is going to be hyper-cyclical, honestly more so than any of the other major sports.
1) NFL - huge emphasis on coach and Quarterback. Get these two things, you could be set for like 15 years as the rest will usually fall into place around it. Otherwise you're wandering in the desert trying time and again to get these two building blocks.
2) NBA - superstars behave like free agents whenever they want, huge emphasis on glamor markets like LA/New York/Miami. League is so crazy superstar driven and the 1-4 draft lotto basically means a lot of teams are just waiting around for the ping pong balls to fall into place in the perfect year.
3) MLB - no salary cap, massive payroll discrepancies mean certain teams are likely to always be competitive if they're willing to pay for it.
The NHL is a lot different than these because it's not one or two superstar team driven. I mean obviously that goes a long way, no doubt about it, but it's never been a McDavid or Bust kind of league as teams routinely win Cups without any top 5 players on their roster. If you do draft a McDavid or whomever, he's probably giving you the ELC+8 year treatment at a minimum to figure it out, players of that caliber aren't going to unrestricted free agency that often because they aren't picking and choosing a specific market or know they are going to get like half a billion dollars.
The teams that are stacked and awesome now probably won't last very long, as the run of salary cap has shown. Even the teams with long runs of contention don't last *that* long in the grand scheme of things. Unlike the Dodgers, they can't just commit big payroll resources (that then incentivizes players to go to free agency to begin with) to always stay ahead of the competition.
When you are a "rebuilding" team, you basically give yourself the best crack at having the players that will be in that 26-31 year old age window for multiple reasons. Most obvious, you draft early and you draft often. Even the ultimate failed rebuild in Buffalo used back to back 2nd overall picks on First Line Stanley Cup winners. That's 2/3 of a Stanley Cup winning first line right off the bat! They just botched it management wise. The other thing you're doing is clearing out your roster and future cap space to allow players to emerge into those roles. Who is your first line in 7 years? Hopefully the guy you picked 1st overall, but aside from that, who knows, open competition amongst all your other draft picks, or you can get a UFA/Trade when the time is right.
The teams winning now? Their draft slot was super low to begin with and then they were probably trading away their draft futures to lever their team for the here and now. This is well worth it, those draft picks aren't that valuable based on their slot, even if they do hit they'll take forever, and you can trade that capital in to help your star players today. This is a snowball effect, like "wow, look how good those teams are, they have all this depth, that marquee player they traded a 1st for that was close to UFA? Now he's locked in for another 8 years because guys want to play on winners." This certainly makes them more daunting of an opponent today... and is exactly why a half-in approach is pretty doomed to fail. The contenders are way ahead right now because they drafted McDavid, MacKinnon or Barkov or even Kucherov or Sebastian Aho in the 2nd round all those years ago (hey remember what the Hawks were doing when those guys were getting drafted?) and now they're leveraging futures to build out the test of the team around them. You try too hard to chase these teams and they'll just bump right into them and get slapped right out in the early playoff rounds. Any player you traded for may not believe too much in what's being built and decide to look around elsewhere as they approach UFA years.
What you can do though? Wait them out. Worth it or not, when you aren't picking early or often, it means there's very unlikely to be a "next wave" coming in. Every once in a while, someone bucks this trend, and good for them, they're the exception to the rule just like Buffalo. What they do have though are a bunch of players that signed UFA extensions from a time when the team was contending, eating up the roster/lineup/cap spots into their mid-30s with Full NMCs that prevent flexibility. Eventually their teams plateaus, then tries their best to keep it going with a series of even more leveraged moves just to remain relevant, they run out of cap space and have little depth around their older stars, then their players decline, and now they're right back where they started.
The rebuilding team though? They have all the cap space to add those new depth players. Their former draft picks are now hitting their prime and the clean cap means they can pay them whatever. They've seen what's emerged out of the excess picks. They likely have a bunch of stuff they're willing to part with in trades. They can go target other players around their best players age and grow into it together. Free agents want to come there, you can trade for guys and have confidence they're going to extend. The winning teams now are likely in their own tank cycle.
This doesn't mean you just Draft a player every year, wait around and do nothing. But it does mean you're being selective, staying flexible and making sure if you are targeting players, they're on roughly the same cycle as your best players. Did Florida draft all their players right now? Not in a longshot. What Zito did extremely well though is maximize a particular window. If you look at their roster, their players are overwhelmingly in a very tight age range. There's some luck there along the way, but instead of just going stuff to do stuff, they targeted players all around the same age as their best players and went from there. It's not an accident that they have 3 of the top 4 picks from the 2014 Draft. That's knowing which players to target in order to maximize a particular window of time. It's the right mix of patience/waiting to strike and not being a "do nothing" team that just waits forever for the "kids" to save you.
17 Evan Rodrigues (1993) 16 Aleksander Barkov (1995) 13 Sam Reinhart (1995)
23 Carter Verhaeghe (1995) 9 Sam Bennett (1996) 13 Matthew Tkachuk (1997)
27 Eetu Luostarinen (1998) 15 Anton Lundell (2001) 63 Brad Marchand (1988)
10 AJ Greer (1996) 92 Tomas Nosek (1992) 12 Jonah Gadjovich (1998)
42 Gustav Forsling (1996) 5 Aaron Ekblad (1996)
77 Niko Mikkola (1996) 3 Seth Jones (1994)
88 Nate Schmidt (1991) 7 Dmitry Kulikov (1990)
72 Sergei Bobrovsky (1988)
41 Vitek Vanecek (1996)
The draft is your Foundation for how you maximize a particular timeline of players. Get the first leg up on acquiring them via the Draft, then you can start swapping and levering to add others that are in that range. Right now the Hawks "range" of targets should all be players currently in ELC age, they aren't likely to be available today (outside of the case of say an Isaac Howard). Getting too aggressive will be a foolish plan but waiting to strike at the ideal time to get players say 2004-2008 birth will likely mean great things will be going on for the Hawks by say 2032.