In a free market, if you spend more than you have coming in the door and don't make a profit, you go out of business. The "market salary" for coaches has no basis in economic reality. It's like you own a company that loses money, yet you pay yourself a big salary. Only your parents are floating you.
You continue to retreat to this inadequate answer and off the mark example, while you ignore the elephant in the room. If you just look at dollars, Ohio loses what, $20m a year on sports? Why do they bother? Do they just like losing money for the fun of it? Or, do they play sports because they feel that a successful sports program benefits the University in other ways? If the only thing that matters is cutting the amount the University spends on sports, slashing all the coaches to half their free market price saves peanuts compared to the very large amounts that could be saved by dropping to Division III, or to club level.
That leaves an obvious question, which you continue to ignore. Why doesn't the University do the obvious thing, and drop football entirely, or at least drop to Division III? There is only one plausible answer, and that is that the University believes that football is operating at a net profit, when it includes other benefits such as attracting students, marketing the University, building closer ties with the town, and building closer ties to alums, who in turn end up making contributions to the general fund. If the University believes it is making a net profit, your whole argument goes out the window.
Once you factor in other benefits, it seems your comparison to a company that loses money is far off the mark. Let's try a different example. Take a company that manufactures products for the space program (at a loss) and related products for consumers (at a profit). Since the division that makes things for the space program operates at a loss, why don't they close the division, or slash the pay below market value for those involved? Maybe they view the participation in the space program as something that raises their prestige in the eyes of consumers, and thus it boosts sales and market prices for it's consumer products, and thus that division is a net positive contributor to the business as a whole, even though it loses money when viewed on it's own?
When it comes to why Ohio has a sports program at all, there are only two possible answers. I opt for the view that they view the sports programs as having additional benefits for the University. It would seem that you view them as simply stupid, yet oddly, you don't seem to favor eliminating sports entirely, nor taking them down to Division III, where there would be very, very significant savings.
As far as the question of whether coaches salaries are currently set by the free market, of course they are. It is also true that the free market for coaches salaries may be distorted by the lack of pay for players. In time the impact of that will work it's way out of the system, and there may be new standards for pay. Whether the free market makes coaches pay go up or down, Ohio should adjust theirs accordingly. If the NFL is any guide, players in the NFL are well paid, but so are coaches. I make no predictions as to what will happen in the future, of than to say that it is possible salaries will change, but it is also possible that they will not.