Yes, it is the coach's responsibility to win each year. Where the good of the sport comes in is the rule set. If the coach wins by breaking the rules, that is bad for the sport. As a result there are remedies for coaches who break the rules. And the remedies are designed, or should be designed, to make non-compliance more penal than compliance.
If the argument is that the rules are bad because there was an outcome that the rule makers did not anticipate, then there is a remedy for that as well. Change the rules. As a matter of fact, we have seen massive rule changes in the past year alone, from how matches are scored to what it takes to qualify for the tournament, and what the seeding criteria are.
And in this very instance, both the new qualification rule and the new seeding criteria came into play.
Meanwhile, from a "pure casual fan, good of the sport" perspective, it is much better to have a three time champion who is going for four and did not receive any preferential treatment, in the the NCAA tournament, than to have a wrestler possibly make the tournament on a technicality after a season of results that do not justify his inclusion.