No, if they reduced salaries it would just go to the owners who would bank it and still make them play more games to make them more money.
I would far rather the money from football went to the people who make the sacrifices, do the graft, take the risks with injury and burnout, and take the abuse from cnuts online than the leeches who control and own the game.
Professional athletes in popular sports make a lot of money because of public interest and it should go primarily to the athletes.
They are not the only players (pun not intended).
Owners have a role to play in responsible and effective administration of their football clubs. And by owners I mean ownership either by fans or firms or single entities. If privately owned, there should be a significant financial incentive geared towards preventing those looking to asset strip clubs or leverage them with debt to make a quick killing.
Local fans should not be viewed as milk cows only. Clubs are nothing without their home base and efforts to squeeze fans through extortionate ticket prices and merch based on "the players need to get paid" is unfair.
UEFA/FAs have a role to play in making sure the sport remains sustainable. What happened at Barcelona should have never happened, and probably wouldn't have if they didn't feel the pressure to keep up with the Joneses across Europe spending wise. Blame the oil clubs all you want but blame can be spread across the board. Plus there's more to football than the elite: you can't tackle inequality in resources without addressing the pull of excessive player compensation at the top end.
So players should be compensated fairly, yes. But how much they get compensated, how much of the cake they get, should be the result of a conversation and negotiation between players, clubs, owners, authorities, sporting organizations and fans, and the result should benefit all parties. Not the players to the detriment of everyone else.