Yes, this restates the Zelman majority rationale. The problem I have here is that the government is doing indirectly what it is not permitted to do directly. Take my example of the cops influencing a private citizen to conduct a warrantless search. Let's add that the inducement is that they pay the citizen to do this, the way they pay informants for information. This, BTW, has been done in the real world and has come up in court. The citizen is not bound by the 4th Amendment. He may or may not be trespassing, but what he does is not unconstitutional per se. Except it is, if the state induced him to do it by paying him to, because the state may not do indirectly what it isn't permitted to do directly.
Hang on, there's a very clear distinction between your example and vouchers. You don't seem to appreciate the intent behind the action as being different. In your example the state wants to do something, but it is not allowed to do it directly. It then gets a private citizen to do it (through payment, enticement, whatever). The issue is still that the state is seeking to indirectly do something it's not supposed to do. With vouchers, the state seeks to provide education. It can do so in many ways, including giving vouchers to the parents so the parents can decide where to send their kids. The state is not seeking to fund religious activities, it is to educate. It's up to the parents to decide how best to do that.
In your example, the goal of the state is to do something it can't do, and it tries to indirectly do it to circumvent the restriction. With vouchers, the goal of the state is not something it can't do (establish religion etc), the goal is to provide education for the people. Where the parents decide to use the vouchers (religious or not religious) is not a state matter and in fact the state has no preference either way. I think that makes it clear there is no entanglement, even if the parents ultimately choose to use the vouchers on some religious school. The state is not seeking to fund religious schools, it is seeking to fund education, the parents decide where to send the kids, and there is no incentive created to send them to religious schools over non religious schools.
Here, the state is not allowed to indoctrinate children into religion, but it can pay parents who want to indoctrinate their own children?
No, the state is not paying parents to indoctrinate anything, it is providing assistance to pay for education. What form of education the parents seek out is completely up to them, the state is not involved at all. As I said, it's no different than a welfare recipient donating money to a church. The state goal is to provide a minimum level of funding for the welfare of the people. How they choose to spend it is not the state's concern.
This isn't really choice. The kids have no choice. While the state can play no role in prohibiting the parents from indoctrinating their kids, it certainly should not be actively assisting them.
You call it "indoctrination" simply because you don't like what they are learning, but who is to say that sending someone to Catholic school is any more "indoctrination" than sending them to a public school? That's up to the parents. You're right, the kids have no choice, nor should they, and nor should the state -- that's up to the parents.
Welfare money is a bad comparison, because it can be spent on anything. This money must go for education, and the state knows that the bulk of it will go to religious education.
Ok, instead of welfare, use food stamps. Parents can use food stamps to buy things that are not good for them or the kids. Many do. Just because some of the parents choose to spend the vouchers on religious education doesn't mean they all do, and it certainly does not mean that the state is indirectly violating the establishment clause -- the state does not have any involvement in the choice of where to send the kids.
Sorry, but yes. The court got this one 100% right.
The Constitution says that the state cannot engage in religious indoctrination per se. It's irrelevant that someone might term something secular being taught as "indoctrination" because if it isn't religion, it's not a Constitutional issue.
There is no constitutional issue because the state is not pushing or otherwise incenting anyone to send their kids to religious schools. It is providing funding, with absolutely no bias as to how that funding should be used.