Because it will stop being "private", which in this case is a blanket term for elite schools. If everyone goes to elite schools, by definition it's not elite anymore.

I went to a private elementary school. Not only did it not help me in the adult world, it didn't even help me in middle school and high school other than put me in GT classes I shouldn't have been put in, make me totally unprepared for class sizes (there were 11 kids in my sixth grade class), etc. Oh, and they had a no homework policy which meant I could never get used to doing homework and by high school just stopped doing it.

On top of all that, I had the same teacher for all six years who both mentally and, once, sexually abused me and encouraged other kids to bully me.

Not one of those things would have happened if I had just gone to a normal public school. Those, for all their faults, prepare kids to be adults.

But nepo babies never have to be adults.

So maybe we shouldn't send more kids to private schools. We need adults.