Here are the last 10 Stanley Cup Champions no.1 C when they won the cup:
Panthers - Barkov
G Knights - Eichel
Avs - MacKinnon
Bolts - Point
Bolts - Point
Blues - O'Reilly
Caps - Injured Backstrom/Kuznetsov
Pens - Crosby
Pens - Crosby
Hawks - Toews
Besides Crosby, MacKinnon and maybe Barkov, I'd definitely put Suzuki (with a good team around him) in the same tier as those other guys. Toews on a dynasty never hit PPG. Backstrom was injured throughout that playoff run to the point where Ovi needed to help him hold up the cup/Kuznetsov individually isn't better than Suzuki in any aspect of the game, O'Reilly isn't close to Suzuki offensively, and i truly believe if you give Suzuki a player like Kucherov in his prime which he may get with Demidov, he puts up better numbers than Point, plus he's better defensively. That leaves Eichel who I think is ahead of everyone in that tier imo. So Suzuki is no worse than most of the previous no.1 C's to win a cup. The difference between him and them is they actually had a dominant team around them