I think Fr. Hesburgh was worried about the tail wagging the dog, and the perception that the tail was wagging the dog.
One of Leahy's former players told me that when Eisenhower came to campus, he sought a meeting with Leahy, but not Fr. Hesburgh, the president of the University.
Maintaining the "proper" balance, a subjective target indeed, could be much more of an art than a science, and I'm more than willing to view some of Fr. Hesburgh's more unfortunate football hires as misses rather than deliberate attempts to de-emphasize.
Malloy, on the other hand, seemed truly ashamed of Notre Dame's football tradition. I'll be convinced until the day that I die that Malloy believed that an aggressive, ethical pursuit of football excellence made him a pariah among the crowd of elitist university presidents to which he aspired.