For US rights, I'm personally hoping for a split between networks that does NOT involve NBC Universal.
In the four major sports, the NHL on NBC is the only one where how often you get on national TV is NOT a meritocracy. What I mean is, for all those decades the Warriors were terrible, they didn't sniff national television. Then during the run of five consecutive finals they got on national TV all the time. When you're good, you get on TV. The League and its broadcast partners showcase the best teams.
When the Jacksonville Jaguars suck, they don't get Sunday Night/Monday Night games. When they are really good, they max out their Sunday/Monday appearances. The league and its broadcast partners showcase the best teams.
Yes there are exceptions, e.g., the Cowboys get more national tv appearances than other teams that are similarly situated, i.e., a Cowboys team coming off a 1-15 season will get more national TV games than a Florida team coming off a 1-15 season. But for the most part, you win and you get on TV, you suck and you get the boot.
The NHL on NBC has been a different animal. They focus so much on just a handful of teams, mostly the Northeast base plus Caps, Wings and Hawks. Even in non-pandemic years, the single NBC Game of Week rarely deviates from this formula. If you're a team outside of this group, you're only hope to get a single national game of the week (note: not regional coverage days, just the single national game of the week) is if you are playing one of those teams. Doc Emrick, the long time #1 voice of the NHL on NBC, never called a Sharks game for NBC except for the playoffs, and even then that's limited to conf finals and SCF. That's like saying in 15 years of Fox on NFC, Joe Buck never called a Arizona Cardinals game in the regular season. It just doesn't happen...except in the NHL on NBC.
The Winter Classic is the league's single showcase game, and although it shouldn't be this way, it's a miracle that the last one was Dallas v Nashville. And although starting on Jan 1, 2008, the game has yet to feature a Pacific Division team (even as the road team). The LA Kings won the Cup in 2014, and the Jan 1 2015 Winter Classic was essentially promised to the Caps. The Defending Cup Champs at Caps was such an obvious matchup to book. In the NFL, NBA, etc, that's what they would have booked. Classic West coast vs. East Coast matchup, two good teams, THE DEFENDING CUP CHAMPIONS, etc. Seems obvious. Instead, it was the Hawks playing in another WC at Caps in what people said was a dud.
Now you can tell me a FOX/ESPN shared deal won't be any different. Maybe it won't, but I know for certain that if the NHL remains with NBCUniversal, it 1000% won't change. It's time to mix it up, and while you're at it, bring back two AWESOME theme songs, the NHL on FOX and ESPN National Hockey Night.