I disagree with your reasonings for the soul reasons of you are undermining what this sport has taught us all. It has taught us to be a man or woman (its 2013 almost 2014 girls wrestle now) of honor and dignity. You lose a close match? Get up compose yourself and shake the kids hand that beat you, you may not agree with the loss but the fact of the matter is that you did lose. The kids will be kids argument shouldn't even be an argument if the kid was coached right even state champions know how to lose, heck even the all mighty Dan Gable knows what a defeat is. And if you think it is gross to shake a sweaty,bloody, and or crotchy hand, how do you coach? this is a sport of all of those things, we all have gotten dirty from time to time and know what it is like to be those things, it comes with the territory. And as for the different sports reason, come on now. Every play in football is not at all comparable too a match in wrestling, it's a single persons match that's their "game". They are going to face another person who it's their "game". Wrestling is a team sport as individual and should be treated as such. Shaking hands is the least you can do to a person who has bested you and shaking his teachers hand is a sign of respect in my book, even should you best someone shake his hand for his handwork he has put forth and his teachers hand for teaching the kid about hard work
If you don't want your kids shaking the other coaches hands thats fine they shouldn't have to. I believe they should but we are all entitled to our own opinion.