I assume that this question refers to the wages paid to coaches of state schools. It would not make sense if it referred, for example, to NFL coaches. I will base my answer on this assumption.
Some people would argue that the compensation for these coaches should be set by government because these coaches are public employees. They say that it is simply wrong for people to get huge salaries for coaching games at a time when governments are hurting for money and are having to cut various kinds of services.
However, if we wish to argue against this, we can say that market forces are a form of democracy. We can point out that people “vote” with their dollars when they support sports programs in various ways. Football coaches, for example, are paid so much because their programs tend to be very popular. Students like to go to games. Alumni pay good money to go to games and often donate money to the athletic programs. These donations and the revenue earned by the football programs (from ticket sales and TV contracts) go to pay the coaches’ salaries. By paying for tickets and donating money and buying cable packages that show lots of college sports, people are essentially voting higher salaries for the coaches.
Thus, we can argue that the people consent to the salaries these coaches receive in a relatively direct and democratic way. We should continue to allow these sorts of market forces to determine coaches’ salaries because they are just as democratic as letting elected officials set the salaries.