Not if 04-05 walkout ends differently. If OLN hadn’t made the decision to change from the the Tour De France/ fishing network to a full time sports network the NHL comes out of that strike going a year and a half without a single game televised nationally, and the only national TV contract they have will show less than 1% of the regular season and 25% of the playoffs, depending on how NBC wanted to use those 20 games there was even the chance the Cup could be hoisted not on TV. In that situation they almost certainly lose the Cup. So then the most well known trophy in the sport goes to some other league, how could you not call that league the major?
Not all the major sports have support from the government. In fact really just the NFL and MLB do. And baseball as a whole is bleeding audience, MLB could easily lose its standing as a major league (ironic that) without even getting replaced by another baseball league.
Soccer probably gets more government sanctioned support than American leagues. You never see the NFL get somebody fast tracked on citizenship. And the amount of money Brazil spent to host the WC would rebuild every single stadium in the NFL with a couple billion to spare.
I see baseball players get preferential immigration treatment all the time, but we are getting into the weeds, and there is no point in arguing about trivial differences.
I'm not as certain as you that the '04 NHL walkout was as potentially catastrophic. That simply is a difference of opinion. I do remember the hand-wringing about it, though, at the time.