I would agree that if all schools in a conference stopped recruiting, they’d all in principle be equally bad. But a lot of Ivy alums (including, I suspect, many generous ones) and students don’t want to attend football games where both teams might lose to a talented high school team. They also like it when the basketball team gets past the first round in March Madness, when the hockey team goes to the Frozen Four and the crew team (and yes, they do recruit oarsmen) wins the national championship, all of which have happened recently with Ivy teams. Precisely because these schools are bound by the AI, they feel able to write off other schools as athletic departments with colleges attached and feel proud of themselves. And I don’t mean to neglect women’s sports - fans love them too, and are proud when team members go to the Olympics (which also happened recently).
I would suggest, too, that another aspect of this debate is being neglected: that a proportionally large number of Ivy student athletes go on to become quite successful - notably in finance. This point was brought out by former Princeton president Bill Bowen in his book (with James Shulman) called “The Game of Life” (as quoted by Malcolm Gladwell in his very insightful essay, “Getting In” (https://www.newyorker.com/magazine/2005/10/10/getting-in))
These schools want some number of people like that, who are going to become successful, reflect positively on the school, be able to donate generously and provide a leg up to future graduates - as distinct from brilliant scientific researchers and all the other kinds of people that the Ivies will be proud to have as alums. The Ivies are all about educating future leaders and increasing their power and reach across society. Sports and athletes are an important part of that.