No. Football is one of the few professions where the players actually get paid close to the true value of their labour.
As basically best players = best results = maximised revenue, the best players hold the negotiating power to capture all the profit from football. Clubs are very unprofitable in general for their revenue and I think it’s better that players get this share than owners and shareholders.
You can’t compare to public sector, so don’t. Compare to bankers, lawyers and other private sector professions.