What if we left World Championship as it is, but replaced the NHL All-Star Game with the World Cup? And I do mean cup, as in elimination-only tournament.
The All-Star Break (now World Cup Break) would last six days (just a little more than now):
Day 1: nothing (maybe a quarterfinal draw)
Day 2: quarterfinals (8 best international teams playing each others)
Day 3: nothing (maybe a semifinal draw)
Day 4: semifinals
Day 5: third-place game and final
Day 6: nothing.
Granted, no round-robin might devalue that makeshift tournament a bit, yet it will still be way more entertaining than the current All-Star Game is, and it will still be the best-on-best format... And yes, some teams will get unlucky... but with World Cup being held every year, it won't be that horrible.
Now, how do we determine 8 best international teams? The first year, we can use the IIHF World Rankings, and then... why not have several Tiers, with promotion/relegation? We can have Tiers A-C, even A-D... why not?
In each Tier, the quarterfinal losers will play in the semifinals, and the semifinal losers will play a relegation-avoiding game on Day 5... the loser of said game will be relegated to the lower Tier.
Likewise, in each Tier but A the winner will be promoted to the higher Tier.