Listen up, I have a master's degree in educational leadership and served as a high school administrator. I think I am qualified to make a statement such as this without having to give a specific example that you would not believe anyway. I studied all types of schools for 3 years in graduate school, attending sometimes 6-hours of classes after I put in a full 8-hour school day.
But just to sooth your wounded pride, I'll give you these:
Try to see if the Bolles School in Jacksonville, Florida has ever accepted vouchers from the state of Florida. They won't because back when I worked in their area the tuition was $26K per year, I have no idea what it would be today. A $4K voucher back then probably wouldn't get you a reply letter to your application. I can't blame them. Would you forego $22K in tuition to help some poor kids living in the Northwest suburbs of Jacksonville a chance at a school in ritzy San Marcos neighborhood with the millionaire elite?
At that time of vouchers, Jacksonville had one Catholic high school. The waiting list was a long as the number of students enrolled. They never took a voucher student. The Catholic Diocese built a new high school on the western side of town. It was full and had a waiting list on day one. They never accepted a voucher student either. That's three!
When I taught in a rural Kentucky county, the population had a higher than usual Catholic component and an extensive Catholic school system. Guess What? There were two public high schools that were fairly decent, so the parents sent their kids to the public schools, so there was no Catholic high school except in another city, two counties and over 50 miles away. If they were given vouchers, where would those students attend? No private high schools existed.