I think the "per capita" bit is misleading. Because it lumps in certain area with other areas.
Certain school districts are way underfunded compared to others. Part of that problem is that a lot of school districts are funded through property taxes. Which has a way of reinforcing the cycle of poverty.
Your voucher system would simply exacerbate the problem. You know what happens when you allow people to be selective about their schools? https://en.wikipedia.org/wiki/White_flight
In your case, it would just be a move to private schools and if you don't think those people wouldn't be able to vote out all taxes that go to schools now, then you are naive.
And breaking up the teachers' unions? Yeah. That's a race to the bottom. Already schools in those underfunded districts do their best to discourage long-tenured teachers as their pay is directly related to years of service. Make it easier for schools to churn teachers and that's exactly what you'd see. Not a selection for the "best", but for the cheapest.
Education is a service with no direct material benefit. Investing in it does not pay off any particular person or group in any noticeably tangible way. However, having a well-educated population benefits everyone and everything.
Education is one area where we probably need less privatization rather than more.