There's usually gifted programs in poor schools as well. This isn't a private vs public education thing. It's more about keeping bright students stimulated and not bored to tears and have their potential stunted.
"Black students are 66% less likely to be identified as gifted compared to white students with similar test scores. Black, Latinx, and Native American students are far less likely to attend a school that even offers a gifted program. These are just some of the issues with which the gifted education field must grapple. "