We are already in the situation where some schools are better than other schools (regardless if they are private or public). This wouldn't change with a voucher system. It is impossible to have perfectly equal schools. Some teachers are better than others and that will always be the case.

Currently kids in the inner city are poorer and stuck in the crappy public schools. Even if their parents wanted to send them to a different school they couldn't afford it. It seems clear to me that the current system is not working for the poor and lower middle class.

The worst case situation would be nothing changes for kids in bad schools. They were going to bad schools and continue going to bad schools. The best case scenario would lead to some kids currently in bad schools going to better schools. This would allow them to get a better education which would be impossible in the current situation. I won't deny that some kids would still be stuck in bad schools, but I fully believe some will get out.