> wealthy parents (and only wealthy parents) figure out ways to supplement or move their kids into schools that are appropriate for their level.
Not true. AP courses and magnet schools are the sole way for working class/poor students to get ahead in life in the public school system. Myself and many friends took advantage of this, and zero had wealthy parents. Many had food scarcity levels of poverty at home but received excellent educations due to these programs existing.
Heck, private schools also participated in this - giving out test and grade based scholarship for exceptional students from poor socioeconomic backgrounds. Many friends participated in such programs, even to the point of working "jobs" for the school after classes to pay for their education. This is now seen as abusive to many.
The ironic and incredibly frustrating thing are now these programs are being systematically dismantled over the past 20 years in the name of "equity" with these trends only accelerating.
The one thing it DOES require is parents who care and give a shit about their kids. I suppose if you squint that's a form of wealth, but not what people mean when they talk about such topics.