Students in private schools are on average going to come from wealthier families than students in typical public schools. But it's not really the students themselves who are the topic of this idea. It's the parents. If you were the parent of a child, and if you really cared about that childs education, and if you had wealth, and the power and political pull that tends to be associated with wealth, would you not make an effort to fix the shortcomings of that school however you can?
This isn't about harming the good students, it's about everyone having skin in the SAME game, so that those with power will be incentivised to pull up the quality of all schools for all students, instead of them just using their wealth individually to cure their individual problem (quality school for their kids).
Everyone already has equal opportunity, hence the public school system. Like you said, it's the parents. It's possible to come from a poor socioeconomic background and to go to an inner-city public school, yet still excel academically. Look at Dr. Ben Carson... he went to a really crummy inner-city high school in Detriot, but he actually cared about his education and is now one of the most renowned pediatric neurosurgeons in the world. The point is: mixing socioeconomic classes may increase the level of "opportunity", but NOT results.
My highschool is ranked nationally around 50. If you sign up for Molecular Genetics, you get to use a $150,000 DNA coding machine that was donated to the school by a chemical company. Again, this is a public school in an outrageously wealthy suburb. Our school was renovated about 15 years ago, so it essentially brand new. I am privileged to not only be in a brand new school, but to have a school with extremely expensive equipment. Now, I also know TONS of students in below average classes and failing these below average classes. They may be in lower level classes, but they have the same great teachers. Their teachers also teach AP Biology, Multivariable Calculus and so forth. BUT THEY STILL FAIL, even though they have the same above average resources. Why? Like you said, it's the parents.
Keep in mind, my public high school is an "elite" high school, and it still has a decent amount of students doing poorly. Now to put this no private school idea into perspective, all of the high schools would be average. Out of the total population, only a few percent of families are "rich". My school has lets say: 40% rich families, 50% middle to upper middle class, 8% lower middle class, and 2% lower class. If socioeconomic classes are distributed evenly, then these statistics (or the upside pyramid shape they form) will be reversed (2% rich, 8% upper mid etc) and instead form a pyramid of socioeconmic status.
It's all about the parents! No matter where you put the damn kids, the ones that want to succeed will succeed, and the ones that don't will not. The smart kids will take the smart classes, the dumb kids will take the dumb ones. Yes, there are kids who want to do well but instead fail because they lack resources. But, those are the only kids you will help, and comparatively speaking, there are not a whole lot of them.
In fact, if you have a school with extremely high expectations, then you may even have more students struggle because they are being challenged pass their ability. Why take AP World History and work really really hard to pull off a B, maybe even a C, when you can take regular or honors World History and get an EASY A. The AP success rates in my school are much higher than national averages because the classes are designed to be harder than the actual AP, so when the AP test comes around, our school kicks ass. So with my AP classes, the amazing teachers always make the class harder than they really need to be. Kids struggle to get a C or B on their report card, but have no problem pulling a 4 or 5 on the AP. Whereas, other kids I know in other parts of my county take the exact same classes, pull of an easy A, then struggle to pull a 3 or 4 on the AP. Think about it, my school has high expectations and an above average population, and they indeed struggle to do well. So with really high expectations and a population not willing to exceed the expectations,
you may actually be increasing the gap between the failing and succeeding... students that excel will be forced to excel further, and students that don't excel will struggle to meet ends meet... if they already performed "average" in "average" classes, then they will perform poorly in harder classes. Now if you try to argue that the students can always opt to take really easy classes and do well, then you just proved my point. Students will not just do well, they will perform amazingly because they will take advantage of the amazing teachers and resources you have, and others will subordinate themselves. You are creating a super elite that will tower above the rest. Aside from all of the logistical problems with relocating millions of children randomly throughout the state on a daily basis, the practicality of the plan just isn't there: it'll probably make the results worse instead of improving them.
Going back to your comment, everyone will have the same opportunity to a quality education, but the results will not improve, and may even get worse. You can't just put a bunch of fat unathletic dorks on a brand new top of the line soccer field and expect them to do well. Of the 70% of people that graduate high school, only a certain amount of people move on to college, and of the people moving on to college, only a certain amount attend prestigious colleges. And then again, not everyone finishes college, especially in less prestigious colleges. No matter what platform you provide, higher education will always seem to be esoteric. You are trying to use government power and resources to fix a problem that can't be fixed by anyone except the individual. So the whole thought of banning private schools is just beyond absurd and ridiculous.
