Vouchers will open up free markets for education.
Entrepreneurs will see that there is demand (and based on what I know how well public education performs in the inner city, probably HIGH demand) for private education in the highly urbanized areas... and the parents of the children in the urbanized areas will now have the means to pay for private education via a voucher. The profit motive will incentivize the creation of new private educational opportunities where none exist today.
Point out that every kid going to a private school or a charter school using vouchers makes the class size in the public schools one kid smaller and increases the individual assistance.
If you're going to start a business and go into competition with someone else, wouldn't you want to compete with someone who is performing poorly? Good voucher schools will locate in proximity to the worst of schools because those will be the easiest to compete against.
There are also private firms that handle bussing for some school districts. If the demand is there, some entrepreneur will be there.
You’d see a lot of construction equipment at churches, too, building new school wings.