The main concern with eliminating government involvement in schools is that poor kids will not get an education. The first few talking points and then the following ones give more examples of how their lives will be better with private education.
Poor children go to college on scholarships.
There is no reason to think scholarships for elementary schools would not be possible. Every parent would have more money since income and property taxes would drop if the money formerly spent on education was returned to the taxpayers. The cost of education would drop since much of the bureaucracy associated with government run schools. Private schools cannot afford to be expensive. The average private school cost per student is lower than the average government run school cost per student.