It's hard to draw a line through cup winners, or even contenders, like this. San Jose was dominant for years with Jumbo Joe as their top center, followed by Couture, who's 6'1" and slow as shit. Ryan Johansen continues to be a bad example as he's consistently excelled in the playoffs and his absence in the '16 finals was maybe the decisive factor in Nashville losing to Pittsburgh. Toews is a big center who for years (especially over the last 15) was right there with Crosby as the most valuable player in the league. LAK won two cups with their giant Anze Kopitar taking over, not to mention Jeff Carter at 2C. Pittsburgh leaned on Crosby: their first cup 6'4" Malkin won MVP with 6'3" Jordan Staal as 3C. Washington wins in 2018 (ancient history, I know!) with Backstrom (6'0"205lb), Kuznetsov (6'1" 205lbs), and Eller (6'1" 207lb).
Even this year, Brock Nelson was and has been way more impactful and effective in the playoffs than Barzal, for example. Barkov was the better player head to head in his series against Point.
To my eyes, what makes for sustained success as a team comes down to being the best at what you can be the best at. The Lightning have 6'6" Hedman and surround him with a bunch of other giants on the blueline. Sure, they have small, quick centermen, but that's more or less the template--the important point is that they have their vision, and they stick with it. Their lineup is basically the same line over and over. Kucherov-Point-Palat, Stamkos-Cirelli-Killorn, Coleman-Gourde-Goodrow. That's like the same exact line 3 times, obviously with differences in skill and scoring prowess, but still. And it's the same on the backend.
If the Rangers really were to have Eichel and Zibanejad somehow on the same roster, it would absolutely be an advantage. But the Rangers certainly wouldn't play the same way that a team that has Point-Cirelli or Aho-Trochek for example.
Smaller centers have an advantage in quickness, but big centers have advantages of their own. For one, I think they are much harder to close on in transition up the ice. Like Barzal has made a living dancing through the neutral zone and crossing the blueline with the puck, but he's also really inept at taking the puck towards the net. He's really meh on the powerplay. Like comparing Barzal with Tavares, Barzal looks a lot more effective, and that rookie season when he outscored Tavares, many could guess he was their better center. But Tavares, big and slow as he is, is way smarter, stronger, and can create dangerous plays with way more frequency, particularly on the rush.
Take this play by Eichel. How can anybody watch this and tell me this guy can't skate with a Barzal or Aho? Maybe in the small ice, but then, where those guys can get inside position on a big center more easily, a center like Eichel has the reach and smarts to basically box out that player with the puck and always be in position to win it back, even from the outside. On this play, Eichel is showing what I mean as far as size giving centers a huge advantage driving the net compared to smaller centers. He's so much more difficult to take the puck from or contain to the outside. Philip Danualt, a player in exactly the model you're talking about, is in the frame there, totally neutered by Eichel's speed, the range of his puck control, and the velocity of his shot.