Have I told you lately that I love the way you ask questions?
The biggest difference between coaching football and teaching self-defense is in how you test it. Every game is an experiment, and they are predictable and numerous. Looked at that way, a coach no more needs to be a player to learn and improve than a scientist needs to have been a lab rat.
Violence is a little less predictable. There is less experience of it; second-hand experience is far less reliable (people practice watching sports and get pretty good at reading the field, even on a TV screen- compare that with trying to get a useable description from a witness). Games are filmed with multiple camers run by professionals, real violence is always caught accidentally and rarely has more than one angle, or good sound or proper lighting.
Violence is also less limited. There is pretty much one type of football game, but just in a hostage situation the dynamics are different by whether it is a mental health issue, a felon attempting to escape, an extremist, an act of rage or a true terrorist siege... and those are different depending on number of hostages; and number, organization and equipment of hostage takers... and none of those have much in common with rape survival or domestic violence.
So in this aspect, without practical experience (and a lot of it) the football coach either knows what he is talking about or can find out, whereas the SD instructor is guessing or turning to sources that may be no more reliable.
One more difference- by the time the NFL coach recieves a player, the player has been in the game, getting hit for years. The player knows the environment and has adjusted to it so that his adrenaline is under control. He knows what a real game looks, feels, sounds and smells like. Some of these most basic, basic things the coach doesn't have to teach- anyone worthy to be coached already knows them. Compare this with the combat experience of the average martial arts beginner. Often never been terrified, never been injured (the basic environment of an assault). I believe it compounds the situation when the person teaching them how to deal with fear and injury has also never been injured or terrified.
The big mystery, Norm, is that a coach or teacher or sensei can teach a student how to move, but does it take something else to teach them how to let themselves move when every fiber of their being wants to curl up in a ball and pray for it to end?