Several of your assertions are unfounded, despite the argument itself being near-sound.
First, I am one of those you speak of. We *are* the ones trying to be involved. To the extent that that has expressed as a "reason" against vouchers - we will not be in the public schools anymore being involved and that will make them even worse than they already are. However, we run into a problem many here can identify with. We are fighting against a well funded and legally entrenched and protected class - the (so called) teacher's unions. Said groups are supported by not only tax dollars (a travesty on it's own IMO) but by the companies that make products that could go into the mandated schools if supported by the teachers unions they then fund - much like politicians only messier.
Yes we are taking our ball and going home. And while it may shock you, that i snot only a valid tactic, it is working. I'm in a state with a high and still growing percentage of home-schooled children. As upset parents *in* the system, we were isolated and marginalized "dissidents". Now, as a separate group no longer participating, we are a distinct demographic. Plus, the school system a couple decades ago decided that schools will get funded based on the student-days - the number of students per-day and the cumulative total. So a school with 180 days of perfect attendance of 100 students would have 18000 days of student attendance.
By us taking our collective balls and going home, we wind up in fact "taking" money from the school we leave - and it is having an effect. Schools are beginning to realize they do in fact need to perform better and several are. As a result those schools are now among the "nice" schools.
This is key, and key to vouchers causing positive improvement. Do you think McDonalds would care about your complaints regarding their service (or lack thereof) to quality (or lack thereof) if they were still going to get your money anyway? If you do, feel free to change your name to Pollyanna. ;)
Now, onto your false assertions. The widespread belief that schools are paid for via property tax is false not only in my state but in many. Income and sales taxes account for the majority of funding for schools, and a majority portion of the remainder is from the federal government - which is not collecting property tax (yet). Funding from property tax is a small portion of school system funding. Thus, your assertion that it is "shared equally" is false on the face. Thus, it really is the "rich" paying for it.
Even if it were, the assertion would be irrelevant. We do not benefit equally from it. It is rather disproportionate in outcomes because so far at least the powers that be have not managed to provide the same outcomes.
We don't want to harm the public schools, and they don't need any help in that department anyway. It is hypocritical (and possibly mean-spirited) to say that those who want to pay for their kids' education are just trying to have more money but those who want their kids' education to paid for by other people are somehow virtuous.
The existing system is broken, completely. By way of example, in my state our budget doubled over the course of a few years. The "reason" trotted out was that kids in school doubled in that time. It was a lie. Our system is require to publish those numbers, and they hide it well on the site - and post after the political season is over. Yet the numbers show that the net increase in kids attending school had increased by under 200. In an entire state. That isn't even ONE school. The number of school-age children did climb quite a bit in that period of time, but the actual enrollments barely rose - barely a percentage. Certainly a couple hundred wouldn't justify the hundreds of millions of increase that was blamed on student enrollment increases.
If a private system did such things they would be sued, and would lose. But the courts have held so far that despite requiring your kids to be there for "an education" the state doesn't have a responsibility to actually provide an education. They could literally just sit there as babysitters all day and be meeting their legal obligations.
You've seen very few actual proposals on vouchers. I've never seen one that could be classified as a tax break for the rich. Why? All the proposals I've seen are a flat per-child amount, not tied to income at all. Thus, we would have a "regressive" tax cut in the sense that the more you make, the less of a break it is. How you conclude that giving a family making 18-24k a year 3k to send their kid to a school they want to is a tax break for the rich is beyond reasonable comprehension. The "rich" making, say 150k per year will get far less relative benefit out of that 3k. In the first case it is around one and a half to two months worth of income, in the second it is around a couple of weeks. Perhaps if you seen some that truly were designed to benefit the rich *and not the poor in greater effective amounts* it is because they were designed for the express purpose of making vouchers unpalatable as a concept. Around here we call that FUD.
Perhaps it is the case you have "rich == evil" branded into your psyche and can't take off the blinders to anything that doesn't hurt the rich.
We are all suffering from the degradation of real education in this country. I've got plenty of non-US friends, and I owe much of my good start to starting out in German schools while my father was stationed there. The fluff our schools spend so much time on is optional in countries that are eating our collective lunch, and their expectations are higher. They focus on performance, not a false self-esteem, and the results are self-evident. The education system we have today in this country was not intended to be educational, but controlling. At that is has been doing a fine job. But it is even failing at that now.
It is inevitable that any human organization of significant size will begin to fail and do so either spectacularly or slide into mediocrity under cover of darkness. In a free society and free market, these organizations get seen for what they are and get replaced. Yes there may be a short-term "crash" and in the short term some people will suffer from it. When this organization either is the government or one protected by it, this does not happen for a long period of time and a lot of people suffer for a long time for it - and lessons are not learned for preventing that particular mistake set again. Especially anything that is essentially an entitlement or taken as one.
Now, through this you might think me a fan of vouchers. That is partially true. Would I like to see a tax break for those without kids? Sort of. I'd like to see it not collected in the first place. But short of that, yes, yes I would prefer that childless people not be required to pay for other people's children's schooling. And in case you didn't catch on I am not in that group (have 3 actually), so it certainly isn't a break for me. But it won't happen. For it to happen the state(s) would have to essentially advertise what they are taking to pay for each child by putting that as the annual credit. That level of sunshine causes people across the board to get upset over the poor performance for high prices.
Short of dumping the government control of society through schools, I'd prefer to at least not force non-parents (for whatever reason) to pay for my kids to go to school. Short of that I'd prefer a strict yet simple voucher system. Take the cost per student and make that a voucher. Or even 80 to 90% of it. No restrictions on what school. Religious, secular, science focused, business focused, technical, or even arts of athletics. Your money follows your student. Not as a lump sum to the school, but in the per-attendance system so that parents who find the school isn't living up to the promises made can still leave for somewhere else. Home-school groups should be allowed to make themselves into a distributed school. The precedent for which is already established via the k-12 VIrtual Academy several states have joined.
To make it better, let public schools convert to private ones. Naturally by vote of the parties involved, and with perhaps even a super-majority required.
Your notion to require voucher accepting students is, even if unintentionally, specifically designed to make it worse. That is precisely the situation we have now. Our children are literally being told that the government schools will take them in regardless of what they do or don't do. Do you think that is doing them a favor for when they go to get a job and learn suddenly that hey guess what, that isn't how the real world works? The mandate to accept anyone is one of the primary failure points in the current system. The second flaw is your requirement to only be funded by vouchers. Again, how is this any different than the existing system? We would find that the level of government expenditure to manage such a compliance system would suddenly be ... about the sam as it is now, plus the costs to administer and police the system itself.
We want our children to be able to pick themselves up when they fall. We want them to learn from mistakes and move on with their lives. How can we expect them to do this when we take that opportunity away when it is the least damaging to make? The earlier you learn to see potential consequences (good or bad) for your actions and reason the likelihood and weigh the risks, the least painful it is and the faster you get better at it. How can we expect our kids to learn these things when we put them in an environment that discourages that learning behaviour by removing the penalties associated with the poor choices. We humans learn the best from our own mistakes, and tangentially from the mistakes of those close to us. We learn the least from authority figures telling us these things.
Over time you'll see a dramatic improvement in not just overall education level but in public schools as well. Competition drives results for all but those who are looking to freeload. Surely one thing we can all agree on is that we don't want freeloaders to basically mooch off of our kids. So let the freeloaders get kicked to the curb. It isn't like the kids they are "teaching" or "administering" are being benefited by what they have now. To handle fraud you handle it like any other for-profit or not-for-profit organization. Fraud is fraud.
But those who are freeloading are those in power. They are well entrenched and a legally protected. Even if it is morally wrong and constitutionally illegal to create such protected classes. Thus it is taking a long time to effect change.