To an extent it tracks. No one wants their children to have fewer opportunities than they did, so a ‘rich’ person will probably have to plan on expensive tuitions and other activities. Obviously once you hit the ultra rich this is a rounding error, but for the middle class I see this dynamic at play.

I can afford one private school tuition, I can’t afford 3. Obviously that’s not a requirement for life, but I went to an expensive private school, do I not want my kids to have similar opportunities? Etc.