Here is something that may help your argument.
1. Big time sports are important money gathers for major cities. Least take Seattle for an example; first it has the big three sports draws (baseball, football, and basketball). This is important because these types of sports help bring in large conventions which in turn bring large amounts of business revenue. Thus, along with the business revenue come the taxes, Taxes which include convention use tax, hotel/motel tax (this also includes RV parks and other outdoor parks), and other taxes that the state and local tax commissions can gather.
2. Now this will help you cement your argument (Backup). When you have several big name players on your team then you have what is called a draw. The draw from a big name (e.g. Jason Alexander, Hasselback) helps ensure that your stadium is full for each home game.
3. Here is what the argument is all about; yes the players should be paid whatever a team can afford. Players like Jason Alexander are big draws. People go to the games to be entertained by these star athletes, thus they are in reality no different that a hollywood star that makes $12,000,000 (e.g. Uma Thurmand for Kill Bill Vol I).
4. The idea that they choose to play the game is not important. The idea is that they are doing what they are being paid for, which, is to play a game that the viewing public want to see.
As long as the public is willing to fork out the price of a ticket, a hotdog, a beer, etc. then who are we to complain. As to the cost of the stadium that is something that over time will pay for itself in revenue brought in by taxes (for different venues), ticket sales, and the saling of refreshments along with other sports junk that the ticket buyers may purchase at the stadium. There is a great deal of money that goes through a stadium on game day, and that is what pays the players.
Big name players give you big draws at the box office, so yes they should be paid because of the money they bring to a community.
Pam