I remember when I was in 6th grade at Wilbur Wright Middle School in Milwaukee, WI, and the pastor of my church, which was located across the street, offended my family by mentioning the daily arrival of police cars. He was trying to say that the local Lutheran school was safer than the local public school. Perhaps he was not being a good neighbor, but since I went to the school, I can tell you that it was not as safe as the Northwest Lutheran School, at least not at the time.
Today, after several Milwaukee area Lutheran schools, including Milwaukee Lutheran High School and Wisconsin Lutheran High School, have used school choice and vouchers in order to stay in business, I'd wager there are more police units showing up at some of these once-elite private schools as opposed to The Milwaukee School of Languages (the school that emerged from Wilbur Wright).
If you live in a traditional big city school district, you'll have some really good public schools (often magnet schools), some really bad public schools, and some private schools that fit somewhere in between. People will pay extra to make sure their own kids aren't sharing the classroom with future criminals. Actually, you kind of want there to be some kind of cost (money, time, or effort). And you want to be able to retain the right to kick any kid out of school at any time. Public schools that can't do this end up with police cars in their parking lots daily. And fewer parents wanting their kids to attend.
In the end, there's a balance. Government money in the form of vouchers versus maintaining the elite status that pressured parents to pay several thousand dollars out of their own pockets in years past. It a very delicate balance, too, because there's a tipping point. If you go the route of Milwaukee Lutheran High School in Milwaukee, you'll end up saving your school, driving the traditional families out to Lake Country Lutheran, and sporting one of the lowest ACT scores in the state. And probably a bunch of police visits, too. However, if your local Lutheran or Catholic school can maintain high standards while accepting enough government money to maintain operation, parents, students, and the school can benefit from a voucher program.