At least the child would be exposed to other ideologies in private school....this would certainly increase his or her freedom to make educated decisions in the future.
I don't understand. Are you arguing the other side?
How would getting rid of private schools hurt the economy? Instead of paying huge tuitions to corporations, parents would just pay the government more in taxes. This should be cheaper overall, since the public schools don't have to run a profit margin and can achieve greater economies of scale.
Average Joe, who does not send his children to private school, has to pay taxes now to send all of these new children there. He can't pay his rent now. Oh crap.
McDonald's now has to pay more taxes and charge more for their BigMacs. Now all of the Average Joes who buy food there can't, and their monthly food bills go up, giving them less discretionary spending and making them less likely to buy TVs and luxury items that would help the economy. Oh crap.