There are many examples of great football players from the Golden Age of football (maybe 20s and 30s) who were high draft picks, but did not pursue a professionial career because it was more profitable to do something else. Without the pay incentive, who is gonna put themselves through the hard work and danger that it takes to be a pro player?
The same thing works with being a medical doctor. How many people would kill themsleves in undergrad to make the grades, kill themselves in medical school, and wipe themselves out in residency to become a doctor if the pay wasn't great? Nobody would.
Relating back to coaching, without the pay incentive that comes with teams performing at a very high level, coaches would put their unique skillsets into something that would maximize their earning. As a society, we need to reward high-performing indiviuals in professions that we place a high priority on. How many of you are willing to watch bad football on Saturdays and Sundays? Think about it for a bit.
The analogy falls apart when you realize that doctors are needed by society. While I love sports, and recognize there is a lot of good that comes from sport, I also don't deceive myself into thinking that it is fundamentally about anything more than entertainment and dollar signs. These men work extremely hard at what they do, absolutely. But there would still be plenty of men that would be willing to do it because they love it, even if they weren't getting paid tens of millions of dollars. Nebraska fans should know this better than most with our walk-on program. Meanwhile, the average family in the world has to try on live on less than $2 per day.
Not to get on an ideological soap box, but I just can't see any way of reconciling the reality of our enormous excesses in sport and just in our culture in general when the stakes are so high and people have so very, very little.
The fallacy is your argument is that you assume that you know what is "needed" by society. "Needed" is a relative term. People lived for millions of years without professionals with the training or medical supplies/technology that we have today. You still have plenty of people living in parts of the world who are untouched by any kind of technological advances that rely on the "skills" of, for lack of a better term, shamans.
If that example is a bit far-fetched, consider, again, the necessity of medical doctors. Using myself as an example, I haven't been to the doctor for any medical work in over five years (illness, injury, etc.). I have been to an office for physicals that were usually performed by a nurse or once by a physician's assistant. At that, roughly 90% of those tests could be conducted by an individual with very little, yet specialized training. On the other hand, I watch football every Saturday for 4 months out of the year. To me personally, the services of football coaches hit closer to home. I am more able to realize the services of excellent coaching.
I also disagree that normaly guys would be willing to coach at high levels for very little. First, within a short period of time, they would overinflate their own value and feel the need to leverage their position into higher pay. Second, look at the carousel of highly qualifed coaches that DID NOT want the position after Bill Callahan was fired. They didn't want the pressure/expectations associated with the job. Average joe working middle management would love the job for about a week and then would melt under the pressure and need to taken out on a stretcher.
It is unfortunate that society allocates their priorities the way that they do, but until you and every single one of your friends, and every single one of their friends, etc. stop giving the attention to entertainment the way that they do, be prepared to deal with this situation for the long haul.