Honestly, I think that primarily goal is academics is mostly lip service. Outside of FB and BB, the Ivies tend do compete well with best in the nation (similar to wrestling). Most of the high level athletes would not stand a chance at Ivy league admission without their athletic accomplishments. They may be better much better than average students compared the collegiate population as whole, but for most athletics is more important than academics
They do have a few official rules like no redshirting and no grad students competing and a few specific FB rules - freshman cant play varsity (not sure if this rule is still in effect) and the FB team cant go to the FCS playoffs.