Why does regulation reduce the quality of private schools that participate in voucher programs?
Individual private school leaders decide whether to participate in voucher programs each year. The decision is made by comparing expected benefits to expected costs. The primary benefit associated with voucher program participation is, of course, the additional voucher funding. The main cost of participation is additional red tape. Private schools that participate in voucher programs have to comply with many regulations such as admitting students on a random basis, requiring all teachers to have bachelor’s degrees, and administering state standardized tests.
Of course, what DeAngelis wants is for government to back off on its regulation of "private" schools that accept vouchers.
That's a utopian fantasy. He who pays the piper calls the tune.
I'm not speculating here. We've seen the same effect previously with the GI Bill, government-guaranteed-or-granted college student loans/Pell Grants, etc. When the state hands out money, that money always comes with requirements that the recipients do things the state's way.
Vouchers don't bring market values to government ("public") schools. They turn market schools into government schools.