And if you take the kids like that from the mediocre schools, or, really, take what money their taxes provide for the school system, you're just leaving the disadvantaged kids to be more disadvantaged.
Let kids move, sure, but the funding shouldn't move with them.
It does, but it's not only that. For a student to excel they need a lot of different things and if they're deprived of any of them they will not do well. In your case, you may see a lot of students with a family/home environment that makes it difficult for them to focus. In other cases a student may have a more supportive home environment but their classmates don't and the slower pace the class may run at as a result leaves the student bored and disinterested.
So a student needs a supportive family, access to proper nutrition, but also a curriculum of really challenging courses that pushes him/her to learn a lot. The latter need is why wealthy parents pull their kids out of public schools.
Essentially, the problem with public schooling is the same one we saw with the mortgage crisis and one the insurance industry deals with all of the time: adverse selection [1]. Students that struggle due to lack of nutrition or a difficult family environment need a far greater share of the funding allocated to the school. Students with strong and supportive backgrounds get far less out of a school that focuses on struggling students. This encourages them to leave, just as an insurance policy that charges the same premium to both smokers and non-smokers tends to drive out the non-smokers.
What we end up with are schools with disproportionate numbers of struggling students. So what's the answer? I don't think there is a single answer. A ton of commentators out there look to education as a silver bullet for class mobility. Yes, education correlates very strongly with career outcome. But education itself is an outcome of a whole host of factors and I strongly believe those need to be fixed, first.
The current system is not hiding or maintaining the problem. The problem is pretty blatant and well known.
Experts don't really know what makes one school better than another. Is it performance on standardized test scores? Improvements on standardized test scores? College acceptance rate?
Even when you do decided on a metric, one of the biggest impacts on educational outcome is parental involvement. Is school A really more effective than school B, or just more effective at attracting involved parents?
If experts have a hard time judging the effectiveness of a school, most parents don't have a chance.
For an example of what this looks like, take a look at for-profit colleges. Through advertising and information asymmetry they attract students who will rack up tens of thousands in student loans for mostly worthless degrees. The most successful for-profit colleges aren't the ones that are the best at educating students, they're the ones that are the best at marketing and sales.
Private schools are usually more expensive because there’s a lower ratio of students to teachers. If all the rich kids left, you’d have schools being merged together to save money; you wouldn’t have the few(er) poor kids left behind with one teacher covering multiple classes.
Genuine question: why do you think the issue of educational inequality is hidden? The problem areas are fully known and there are dedicated charities working to address it all around the world. Is the argument we need to make the situation so worse to bring it into the public conscious more?
The inequality is already there, the current system only serves to hide it and maintain it. Why not try letting go and opening up the door for more students to move around? It would give us a better idea of where the problems are so we can address them.