They have a problem paying for players to go to an event they have seen no economic benefit from. The sports you talk about originate as sports with international competition. All North American sports primarily developed with one dominant nation Canada for Hockey, and Basketball, Football, and Baseball for the United States. The primary competition for all sports has historically been the league championships, not international competition. I mean, the NHL existed for 50 something years before any major international hockey event took place.
The NHL is a private business with owners. They have no obligation outside of acting in the interests of their product. You aren't conscripted to play in or watch the NHL. If players don't like it, they can play for less in a league that will allow them to play in IIHF events. If fans don't like it, they can not watch or support the product and hope their support can create a viable other league.
I know perfectly well how the entertainment industry reasons and works. You don't need to explain that part. As you say, they sell an entertainment product. That product happens to be a sport, hockey in this case. The sport in itself is of absolutely no interest to them. If they would earn more money paying people to wear pink leotards and juggle with kittens for 60 minutes, they would do it and scrap hockey altogether.
That doesn't mean I like that the biggest "league" in hockey is in the hands of the very cynical, corporate America. Not even in the slightest. It's terrible for hockey in itself. Basketball doesn't have the same problem to the same extent, as basketball worldwide is a lot bigger sport. Neither is football suffering because of MLS, not even a bit. But world hockey being dictated by the selfish interests of NHL alone, because their wallets are infinitely bigger than the other leagues combined? That is a huge problem.
Speaking of conscription. What do you call the draft then? It's in the name! The players are conscripts. Well paid conscripts. Either you accept to play for the team that picks you if you want to play in the NHL, which you as a player can do nothing about. Your only choice is to refuse to come over for half a decade, while you will hear infinite whining how "unprofessional" and how bad of a person you are, from both fans and owners.
The NHL is serving the next year of world talent on a platter and they take turns draining the other leagues of their best and most promising talent. In return the real hockey clubs receive coffee money, with the threats of "I give you an answer you cannot refuse. No really, you can't refuse. Either you take our coffee money or you get nothing."
The NHL is an imperialistic cartel, which pretends to be capitalist and competitive. Of course they don't care they're sucking the sport dry.