As a parent who sends our children to a private school I think all states should implement this.
We are paying tuition twice. Once for the government indoctrination school, and a second to actually educate our children.
As a parent and grandparent who has been paying to send kids to private schools and/or support homeschooling starting 40 years ago, I have two responses:
1) In principle, I fully agree. It's the right thing to do.
2) Doing the right thing will lead to its destruction, making it actually the wrong thing.
Expanding on point #2, the government supported private schooling will be attacked from a number of fronts:
1) Any time the government is involved in distributing money, it will leverage this to expand its power and eventually control every aspect of private schooling as it does now with the public schools.
2) Any time the government is involved in distributing money, lazy and dishonest people will find ways to misuse this money, leading to corruption of the system.
3) Because more money is available, private school costs will skyrocket. A repeat of what student loans did to college costs.
4) Private and home schooling is more successful now because those that pay for it are dedicated enough to make the financial sacrifice. The kids all have parents that care. Make the private schools cheap or free and they'll have the same demographic as the public schools.
5) Private school teachers also sacrifice by making less money than public school employees. If they weren't dedicated to the kids and their jobs, they wouldn't do it. Put all the money into the private schools and teaching there will be just another job with money more important than the kids.