I agree but want to correct you on the public school point. Excluding the service academics, there are 2 or 3 schools with sub 20% acceptance rates, and every other public school is above that.

See [1] and [2]. And these are the best public schools. The average of the top50 public schools is probably 40%ish, and the average of all public schools is 70%.

[1] https://www.collegesimply.com/colleges/rank/public-colleges/... [2] https://www.oedb.org/rankings/acceptance-rate/