That’s not now the CBA works. The players get paid regardless of what capital investments the league decides to make.
Due to COVID the league’s revenues have been stuck at more like $4.3-4.5B for a while now. But let’s take $5B as an assumption going forward. The players get half of that no matter what. The NHL gets the other $2.5B to spread amongst its central operations and 32 franchises.
The Calgary arena is set to cost $550M. For the league to pay for that outright, it would have to spend the equivalent of 20% of a year’s revenue (plus interest if structured as debt) on a single capital project for a single team.
This is why they ask for public assistance. It’s not realistic for an owner or league to finance that kind of money for capital, not counting the even larger operating overhead they are already paying.
The league / players split in the CBA is negotiated based on available revenues.
This is not some un-moveable edict set in stone. Local governments have set very bad precedents in subsidizing these businesses.
As for capital projects.. surely you realize they are amortized? So spread that cost out over 30 years, which interestingly enough is close to the number of teams in the league. So the $550m is a good place to start as a yearly league wide infrastructure cost. But that is in Canadian dollars, while we track league revenues in USD. Convert and we end up with $440m.
BUT! most teams either already spend some money on arena rent or own their arenas outright, so it's not like the costs aren't partly being paid. Even the Flames are paying half of the arena.
So let's divide that $440m by two, to estimate what the league would be paying moving forward if they weren't supported with public subsidies. That's $220m.
Then we'll use your number of $4.5bn league revenues. $2.25bn goes to the players. Assuming the infrastructure cost comes out of players salaries, that's just about 10%.
So in summary, players salaries would have to decline by just 10%, from an average $3m to $2.7m, in order to get the league off of public subsidies. Considering that the league has cut salaries by that much or more in two successive lockouts, it doesn't seem like it would be the end of the world.