How do you propose society manage the kids that don't have parents or guardians that care enough to get the kid into and kept in one of the many private schools that would exist and fit the kid's educational needs? Are you going to step in to help these kids? Probably not. How would you manage the kid's need to get to and from school even when the private school that fits is located across town? Are you going to give these kids a ride to their school? Probably not.
Do you really think that these problems are difficult to solve? Probably not.
Putting aside the fact that kids with uncaring parents are unlikely to benefit as much from school in the first place, parental involvement being one of the key requirements for success, I never said that the requirement to see to it that your kids attend some school should be lifted. Whether the parents care or not, their kids will go to one of the available schools.
Arranging transportation is the parents' responsibility. Most cities already provide public transit, and more than a few rely on it for getting kids to and from school. For those few cases where the only schools that fit are outside of commuting range, there are always boarding schools.
It can also accomplish this at real cost, not cost-plus-profit. It seems to me that the private sector normally operates with earning a profit as the highest priority.
There is nothing wrong with having a profit motive; it ensures that you have an interest in providing the best value, as perceived by those paying the bills. In any case, "private" does not have to mean "for profit". An education co-op, for example, is a perfectly viable model for a private school system.
A government-run public school system doesn't need the same level of oversight and regulating given that the system likely is as it specifies.
Do you really believe that? The cost of regulation still exists, as someone still has to define the standards the school is expected to meet, and if you're not bothering to have an outside party enforce the standards, a public school is just as likely to cheat on them as any private school.
In your system, the tax payer is still paying for the education of every kid through scholorships[I read vouchers]
Vouchers imply that the public schools are the default, and those going elsewhere get a portion of the funds that would be spend on their child to attend some other school. Without the public schools there would be no point in calling them vouchers.
Externalizing the cost onto the taxpayer is an inevitable consequence of trying to ensure that every child can attend school regardless of the family's financial state, without relying on (private, voluntary) charity. That is a problem, but it's not one I was trying to solve here.
Again, I believe it is in society's best interest to do what society can to prepare every kid, within reason, for the future. I believe the better prepared a kid is, the less likely the kid is to be burden to society down the road.
I agree with you here. This is why we can't afford to leave education to the public school system.