Maybe, but private schools traditionally pay less than public schools, and have fewer benefits. The advantages usually are more discipline and/or the religious focus of the private schools.
Around here, actually, private school teachers don't have to have a degree or teaching credentials, and some don't, especially at the small Christian schools.
The quality of private schools varies, as well, with some being highly competitive academically and some not even as rigorous as the public schools.
Especially in some rural areas, there are no private schools to compete with the public schools, but the addition of voucher money to the mix might remedy that.
If vouchers would available, I'd expect several outcomes:
1. Some parents who are currently sending their children to private schools could use voucher money to do so less expensively.2. Some parents who can't afford private school could, with vouchers.
3. Some parents would find there was no private school available even though voucher money was available.
4. Many new private schools would spring up. Some would be good, some would be adequate, and some would simply be there to try to get some of the voucher money.
True -- private schools NOW generally pay less -- because less money is available.
Take away the protected monopoly of the current gvmt schools? Money will flow to quality. That IS the benefit of the free-market.