I know the analogue is not exactly the same but consider this:
What about the other big 5 sports? The NBA (soft cap+luxury tax), MLS, and NFL all have salary cap systems.
Out of the most recent 10 championships where a winner was based in a no income tax state:
NBA: 1 winner (Dallas), 2 finalists (Miami)
MLS: 0 winners or finalists
NFL: 1 (Tampa Bay), 0 finalists
Most of the winning teams were actually based in California (49ers, Lakers, Golden State Warriors, Galaxy) or somewhere based in the northeast US.
Someone more intelligent than me could tell me why else the majority of competitive teams are not from income tax-free states - to me this just reeks of NHL northern traditionalist market views and small sample sizes.
I still stick with "good players want to play on competitive teams" theory, and that this is just a small sample size of success and correlation in the NHL that we're not seeing anywhere else.
I will say I only did a quick Google search/Wikipedia lookup as I am not deeply interested in the league structuring of the other major sports but on the surface it hardly seems to be the same issue.