You are like Devos. You have no experience in public schools yet you're an "expert" on the subject.
Do you know what goes on in a public school? First off, retention of students at the elementary and middle grade levels are completely up to the parents. If their child fails, they can still be "passed on" to the next grade simply because Mommy and Daddy don't want them to be held back. They can do this because there are no "credits" for completing coursework at these levels, like in high school. So kids are tested below grade level in 2nd grade, and the parents don't want them held back, then they go on to 3rd grade material and cannot achieve at that level either....and so on and so on.
Also, schools are reluctant to keep older kids behind because of possible scenarios of having older, more mature kids in the same classroom with younger kids. For example, if a kid is in the 6th grade and reads at a 2nd grade level, having him in a 2nd grade classroom would be good for him until he is "caught up". However, that will never happen. Instead, they expect the teacher to teach at different levels during a 50 minute time span to dozens of levels.
Finally, the private vs public school debate is arguing apples to oranges. You make the bold claims that private schools take "failing public school students" and turn them in to scholars. It's easy to make that claim when the statistics are either skewed by not being assessed the same as public schools or no true statistics to back up this claim. Also, private school enrollment accounts for only 10% of American students. And a big guess at which socio-economic class has the majority of private students?? Yep......not the poor. So, when these private schools are evaluated and assessed (bogusly I might add), they are assessing students that have private tutors and see college in their future and are academically motivated for such a life, due to their wealth.
Again, take a kid off the street that has no money or time (let's say they have to get a part-time job which takes time away) to develop a skill and compare them to a person, of the same age, who has the time and money to develop their skills every day through training. When they are evaluated, who do you think will have the higher grade????