That is addressed in the book(this counter argument was my first reaction as well). Charter schools get kids from lottery(demand FAR outstrips supply) well they did research and tracked kids who were in lottery and did not get in. Their outcomes were far worse than those who got in.
My own conclusion from reading it is that few things really make difference: 1. Charters have strict discipline, violence etc is not tolerated in any form. Public school in bad areas are chaos 2. Schools can easily fire teachers who do not perform well. In public school system you need to rape or murder someone to get fired. 3. Shitty charter schools lose their charter and go out of business