The league changes the draft lottery every time Edmonton wins. Hopefully we won't be seeing any changes any time soon (the silly COVID lottery excluded of course).

This isn't true at all. The last no state tax team to win the Cup was Tampa Bay in 2004. That's a long time ago. In the past decade:

2010 Chicago: 41.25% on $5M
2011 Boston: 41.35%
2012 Los Angeles: 49.10%
2013 Chicago: 41.25%
2014 Los Angeles: 49.10%
2015 Chicago: 41.25%
2016 Pittsburgh: 42.37%
2017 Pittsburgh: 42.37%
2018 Washington: 45.16%
2019 St. Louis: 43.30%

They're all in the average range, with the exception of LA which is in a higher bracket. Only Montreal (52.81%), Ottawa and Toronto (52.77%) are significantly higher than LA, with Anaheim and San Jose(49.10%), Vancouver (49.12%) and Winnipeg (49.85%) being in the same range.

This is a far cry from the lowest tax cities in the league: Tampa, Florida, Dallas, Nashville and Vegas are all at 36.3%. No Cup winners in that group. Arizona and Colorado also have lower taxes than any recent Cup winner.

In conclusion, there's simply no correlation between taxes and playoff success.

Barely. Matthews had his contract set up with massive signing bonuses and minimum league salary, because the signing bonuses are paid out in the summer when he lives in Arizona, thus paying 41.21% tax on that bonus instead of the 53.19% he would have owed had he earned the money in Ontario. So Matthews is a poor example because he gets the best of both worlds: low tax environment AND the biggest hockey market in the world.

And STILL Dubas managed to overpay... but that's another topic altogether.