If a few students are given vouchers, the school loses enough money to pay a teacher. That means all of those students are redistributed to other classes increasing class sizes... A school bus with 40 kids on it costs the same as one with 44 on it. The term is called "economy of scale.
Fewer kids = larger classes? Fewer kids = fewer kids on bus?
I don't think your reasoning could be any more self-serving, if you tried.
Given that vouchers leave more money/student for the school, more likely class size shrinks faster than teacher cuts. Same for buses.
Economy of scale doesn't always apply. Given 10 buses with 44 kids, then there could be just 9 buses with 44 kids, if 44 kids leave.
When schools are complaining of over-crowding, your argument doesn't apply, except maybe to work against you.
Let's just pretend for a moment that you have a brain and can reason using mathematics.
In a high school, there may be 150 students taking Algebra per teacher, with 6 classes of about 25 students each. If 10 students leave the school, you now have 140 students. One teacher that was teaching 150 students now has 140, but 140 students do not generate the revenue required to pay that teacher's salary and benefits, so you lay the teacher off. Those 140 students are then required to be taught by someone else. If there is only one other Algebra teacher, do you honestly expect them to teach their 150 students plus 140 more. Of course not, so every math teacher with other classes, now has to pick up one of the laid-off teacher's classes of students. Their 150 students are now crammed into classes of 30 students each because there are now only 5 periods left for them.
We fought overcrowding in the classroom by going from 6 classes a day to 7, but the contact time with the students was cut from about an hour to about 50 minutes. Students and parents complained because we could not give students time in class to work, so the amount of homework skyrocketed.
I started teaching in Florida in 1996. My classes averaged from 30-35 students each in 6 classes per day, so I taught about 200 students. In some schools, students were sitting on 5-gallon buckets turned upside down. Florida got smart and passed a law saying classes at the high school level could have no more than 24 students per class. Performance of the students jumped dramatically when they weren't stacked like cord wood in a classroom.
One of the many advantages that you see private schools advertise is low student-to-teacher ratios. If they start picking up voucher students, what happens to that statistic? Do you think they will hire those teachers laid off by public schools? Of course not! They can't afford them! Their class sizes will grow and many of those advantages they claim will magically disappear. It happens everywhere they try vouchers.
Do you think that check for a $4000 voucher will pay for private schools with tuitions that are double that and more?
How do these kids get to school? Is the single-mom going to drive 20 miles across town in rush-hour traffic to drop their little darlings off at school? Who picks the kid up at 3pm when Mom works until 5pm?
Jacksonville had a great magnet program where kids would ride buses to their local school and then spend about an hour riding to their magnet school in the inner city. When diesel prices started going up, the district eliminated the bus service to the schools. The magnet programs all but dried up. So do you think private schools are going to be able to make this work?
We had 19 high schools in Florida and under the voucher system any kid who attended a D or F graded school could attend any other school they wished with a transfer if the school was not overcrowded or they could attend private schools. Not a single private high school would accept voucher students because they knew the costs would not be worth it. The discipline problems, truancy, and poor academic performance of these kids made it an impossible choice. Also, they would lose tuition money by taking the voucher. It was a disaster from the word go. Fortunately, the state constitution made vouchers illegal and it did not withstand a court challenge. Smarter people prevailed when it was proposed to change the constitution to allow for vouchers. No one wanted them after the myriad of problems they caused.
Were there successes? I am sure there were a few, but the costs and pain of running the program simply was not worth it.