your mother did a great job. in a way its a bad idea, the tax payers will end up paying for it like you said. but it's more than likely the number of dropouts in new york has reached an time high among people who only have one parent. where as they go out to work to get money for the family, so the mayor sees this as a way they can do both, make money and attend school for a better education.
In Ireland, in my local town, there is a school (just one) where as the students are paid to attend it because they dropped out of the other schools. so the state or the school pays them about 80 euro a week to go to class. They sit a special exam at the end though, not the same state exams as the rest of the schools in the town. I think the scheme has worked brilliantly. and all the people I know that are in it are from one parent families. It takes them off the streets but it also means that more and more will go to it because they are being paid too rather than go what I'd call the normal secondary schools