I have had the experience to be a part of both. I was in a private school up until high school when I was given the option to attend public school and I took that options. What I have learned is that there are a few reasons as to why public schools are better than private ones.
Public schools often have better teachers who know how to reach a kid's potential. Charter and private schools in many states don't even require a degree to teach!
Public schools are more in touch with building a community and being part of it. Many parents end up sending their kids to the same teachers who taught them which is great.
Public schools are far more diverse. Kids learn how to work with and get along with different types of people and are far less likely to develop racist, sexist, or prejudice tendencies.
That is just a few. Do you think public schools are better?
There is some validation to what you mentioned here but most public schools across America, especially those in urban and inner city areas are failing hard and fast. Just in my local city alone, I have witnessed 7 public schools close in the last 10 years. Where are those kids meant to get an education if they can't afford private school? Maybe this is true of suburban public schools but certainly now inner city ones.
The thing with private and charter schools is there are less students and more one on one focus for the children. There are also specialty classes that do require higher education in fields of psychology for example.
Public schools are only as diverse as the location. I grew up with only having one or two black students per class. By the time I graduated, 40% of the graduating class that year was black. The reason behind this was that the schools in the intercity closed down and shifted a bunch of black students to my area. The place is run down and crime ridden now and the education in the schools is just awful.
Public schools should be better in theory but poorer locations with hacked funding end up hurting our kids more than helping them. I have seen plenty of public schools do just fine but they are in richer areas where people tend to have money.
Public schools are way more affordable and if you live in a good area where the housing market is stable and there are low crime rates, the public schooling will be on par with private schools. The only time private schools are better is when the public school is in a bad area.