The problem with choice, charter, and voucher schools is that we're all human. Human nature tells us to look out for ourselves, and even if the entity running your organization promotes wonderful morals, those can come in conflict with the results of our humanity.
I recently met someone who was married to a religious school principal. They were now divorced. That happens. The problem is that the principal is now in charge of 100+ students with a black mark when it comes to the religion being professed at the school. It's a lot of pressure for someone like that to avoid personal conflicts. It's worse, of course, when a church employee takes liberties with the kids, and that's happened, too. I'm not saying it's great for non-church workers at public schools to do any of this stuff, but governments should be held accountable to not sweep allegations under the rug, which I have personally seen at church-run schools. That said, I've seen it in public schools, too, but at least there might be some eventual accountability.
The other human vice we should worry about when it comes to vouchers for schools is greed. If greed is what drives a capitalist economy, and capitalism is seen as the best way to administer vouchers, then it would follow that a fully-capitalist version of vouchers in schools would be led by greed. Not that the kids will solely learn about that in the classroom, but the intent will be to make the most money for owners, investors, and maybe employees. It could lead to a sort of educational industrial complex. The problem here is that children are impressionable, and if local governments lack the autonomy to choose textbooks, then what a generation of children learn in our voucher-funded schools could be exactly what those with the power want them to learn. If you though fake news was problem in the 2016 election, what happens when it becomes part of the standards?
When I was teaching in a fairly large high school, I always loved the fact that others in my department had their own personalities and mini-agendas. Nothing too intrusive, and we were all different. Think about how that could change if all schools become based on some corporate agenda. Don't kid yourself into thinking these would not exist. For example, if SchoolCorp runs 5,000 schools and signs a contract with MegaStore. All the tax money going to SchoolCorp gets spent at MegaStore, but, just as importantly, teachers are encouraged to use articles and examples that promote MegaStore. This will happen if schools all go to vouchers. Maybe it's not terrible. Maybe it's expected in a capitalist society. The question is whether or not we really want to find out.