This is silly. Most public schools are designed to retain talents in state. They were never designed to educate OOS or International students. So the main competition here is between in-state tuition and top private elite tuition.
Most top students, except for the exceptionally wealthy or exceptionally poor, are probably evaluating between their in-state flagship (most likely an honors program) and top private elites. Where they go will probably be largely determined by the amount of financial aid received. I think most parents earning between $150k-$300k a year will not shell out $70k a year in undergrad tuition for a private elite when their children can go to a top flight in-state flagship for next to nothing. Not only do these public ivies remain relevant, but they are more relevant than ever.