There is always saying: The customer is always right. So In these three options: the players, fans or clubs, i think the role of the customer is the fans. Obviously, the fans are more powerful, because they pay the money, the players and the clubs are earn the money from fans.
Absolutely fans generates income to them + more fans more advertisement which create another revenue to the team or the league and if there's no fans engagement on the sports then they don't have money to pay the expenses of technical aspects also with players salary so for this the sporting event will collapsed.
That's true, but...
More fans... more sponsors... more revenue, better players... better players, more victories... more victories, more fans...
This is a cycle, which really is all important, but unfortunately today, if you are in a situation that those who have more money to invest, will really be able to master the game better.
Of course, this will not guarantee the victories, but it will certainly guarantee that you are always at the top.