"Some states really restrict private schools from even existing so a national voucher system might be difficult without other changes."
The fights over vouchers and charter schools in DC over the last 20 or so years were epic.
DC public schools used to be some of the best in the nation, now they're among the worst, despite having the highest per student spending in the nation. Of course, the answer from the left was "MOAR MONEY!" With a strong subtext of "you can't let get out of their failing schools for better ones, that's racist!"
If you want to see why vouchers ARE a good reason, take a look at the NEA's opposition: http://www.nea.org/home/19133.htm
The teacher's union/public school cabal has been fighting vouchers tooth and nail in Milwaukee.
It got so bad that a charter/religeous schools wanted to buy up old, abandoned public school building to open schools... so the public schools system, (MPS) sold the buildings to a developer for really cheap and then leased them back to themselves, just to keep them out of the hands of the private sector. MPS is required to sell off surplus properties, which they had a lot of because of declining enrollment.
ETA: Just recently, a former head of MPS was indicted on a charter school scam. He quit MPS, partnered with another scumbag from Philidelphia, and set up a number of fake charter schools to collect money from the state. Its almost as if he did it on purpose to undermine the voucher system.