What do you think is happening in the future of the really smart kids who graduated (from either public or private schools)? Hint, the brightest of our nation's children are getting accepted at our nation's top universities in our nation's best and most challenging programs. Since those schools are turning down over 90% of their stellar applicants because they only have so many spots, that goes to show you that we don't have a shortage of the country's brightest. In other words, there is fierce competition between these high achieving students to get into schools and programs sought after by the best of the best students. These brightest kids are not getting pushed to the side. They are competing like never before, the best of the best are filling those coveted spots and they are then going on to cure diseases, work for SpaceX, etc. You'll never see MIT with a need to seek applicants. Every year they've got many, many exceptional ones than they can accept.
The concept of equity has begun to complicate the ability of the public school system to challenge the top students. These days, some schools and districts are trending away from AP classes, valedictorian status and such, claiming those things create a separation between the best, the middle and the slowest - but, luckily, in many public schools, these programs still exist, and competition is still "allowed". In more rural places where a public school simply can't successfully prepare our brightest for top levels of scholastic success, private schools fill the need or parents understand the need to move for the sake of their talented child.