Just wanted to mention that there is definitely a salary cap advantage for the teams that are in states that have low income taxes.
But larger markets also have another key advantage irrespective of country; higher sponsorship deals and visibility, which also potentially means higher revenue for star players.
It comes with added drawbacks too, like not being able to go to the department store in peace and getting googly-eyed fans looking at you potentially all the time, but that's irrelevant to the subject matter.
Aside from that whole can of worms there is also the RCA, an option that players who play in Canada can use if they want to maximize their earnings. Jarome Iginla did, and it allowed him to take home many more millions over his career in Calgary than if he hadn't done it.
Small explanation of RCA (doesn't go into the details at all but good enough):
Planning for the Future: The RCA and Professional Hockey Players - GBL
The RCA situation is not as straight-forward as no state-tax vs. state tax, but it does give some ways for players in canadian franchises (or high-tax markets) to offset some of the higher taxes on their salaries.
The advantage of a lower tax-bracket that the RCA offers is unfortunately counter-balanced by the fact that the RCA, by its nature as a deferred commodity, generally gets out-performed over time because of inflation by money that could be more freely used by a player to invest if it wasn't tied-up with RCA.
Then we start going into tangents about which states exactly have which taxation brackets, how their respective legislature treats signing bonuses and how they are defined, the payment method of the NHL with its "pay per location and days spent there" structure, more besides, and this starts looking like a "Business of Hockey" mega post that would take hours upon hours to write and much brain power to comprehensively read.
Without getting caught-up in all of that, the short of it in this case is that the no state-tax teams DO indeed have sort of an edge on cap matters, moreso for star players and their contract structures.
Except that this shouldn't ****ing matter.
Even if you don't get 100/100 advantages going your way, a lot of the last winning teams of the last couple of years have managed to make it work even with state taxes.
Yes the game is not perfectly balanced, yes there are loopholes and teams sorta/maybe exploiting them. But with enough luck, good pro and amateur scouting decisions, good team building/identity, and strong coaching, any team can win.
The NHL could always re-balance things a bit, but it is still generally in a "very good spot" comparatively-speaking. We're talking details here compared to other sports.
This is not the MLB, where the game is rigged from the get-go and only the biggest teams have a good chance to win while some others are basically the farm teams of the big franchises and constantly losing their best players once they reach full free-agent status.