You’re mistaken, @ucbalumnus, and you don’t understand the motivating force behind why parents like myself choose private school options for our children. It wasn’t about “removing barriers” “in trying for an elite college”. One, my kids didn’t pursue Ivies although they did pursue and attend selective LACs, although passing on some higher ranked acceptances to choose schools based on fit. Choosing the secondary school path we did was about a better, different and, yes I’ll say it, superior learning environment for those 4 years not a college end game. Don’t mistake my list for removal of barriers (not sure what barriers you are talking about exactly anyway). It wasn’t a cakewalk by any means. As previously indicated by another poster, these students would go to selective colleges whether or not they chose to go to private or public. The secondary school my kids attended was every bit as selective as the majority of elite colleges. My kids would honestly have done well in the college game either way - public or private - as would most of their peers.
The students that are most helped are those who are on FA, especially full FA. Higher SES families have the resources to give their kids EC and other opportunities no matter where their children go to high school. Plenty of evidence of that.
Rather than stereotyping and judgement, listen to the voices of folks here who actually have first hand experience.