The league wasn’t really trying to make those teams move. Betman put in a lot of effort to keep Winnipeg, he was on the phone trying to get a stadium deal while they were packing. Hartford was playing in a mall, that needed to change, nobody’s fault but theirs that change involved a move. The teams that are struggling are the teams that stink, they can’t keep the fan engagement. Those teams are finishing under 500 most of the time, out of the playoff hunt by the All Star break. Edmonton and Calgary went through similar eras and had similar attendance problems. Nobody wants to pay money to watch their team get their asses kicked. The southward teams that put a quality team on the ice (San Jose, Kings, Nashville) make money.
The “big city” bounce for NHL playoffs is minimal. And without a national TV contract NOBODY outside of Chicago and Montreal watches, so there is no possible way that would get more viewers.
The current NHL model doesn't work well simply because they have 30 teams in the league but only about 8-9 good hockey markets. I define a "good hockey market" as a city where the team could probably fill 90% of the seats in their arena in the last week of the season even if they're out of playoff contention. These markets would be the Original Six teams, plus Edmonton, Philadelphia and maybe Buffalo. Winning doesn't guarantee a fan base at all -- as evidenced by the difficulties faced by the New Jersey Devils in the late 1990s and early 2000s even as they were one of the most successful franchises in all of North American sports on the ice. I can pretty much guarantee you that Nashville will go down the same road once the novelty of their success fades. Heck -- the team was a candidate for acquisition and a potential relocation to Hamilton or Kansas City as recently as ten years ago, and it was only awarded an expansion franchise in the first place in the late 1990s because it was the only city among the contenders (Columbus, the Twin Cities and Atlanta were the others) that had a new arena in place to accommodate the team.
I suspect hockey fans lose interest in their teams not because they lose, but because their favorite team loses its top talent to other teams. This is what happened to Edmonton in the early 1990s after every one of the stars from their dynasty of the previous decade was traded or signed away.
I think I read somewhere that the 2013 Stanley Cup finals between Chicago and Boston generated larger TV audiences in North America than the NBA finals that year, but the numbers don't show up in the ratings because Canadian networks aren't included in the U.S. TV ratings.
I think the NHL Board of Governors had been pushing to have those teams move for years. The four franchises that came into the NHL as part of the 1979 merger agreement with the WHA were never really a top priority of the NHL. The immediate success of the Edmonton Oilers (through their sort-of-underhanded methods) probably caught the NHL leadership completely off guard.