If they want to compete with public schools, they should follow the same rules. Finally, what if, in keeping with the mandated Constitutional requirement to keep Church and State separated, religious schools were kept out of the mix. They don't really believe that a voucher system can lead to better schools. They want to divert public money to schools that will teach the narrow range of their social views. They don't like the idea of children learning the wide range of arts and science that will open their eyes to the wonders of the world around them, and give them the ability to make life's choices independently without asking permission.
Conservatives are right about one thing.
You cannot just throw money at problems in our existing public school system. Yes, a larger educational budget would certainly be welcome. It would be nice to restore music and the arts to our public schools, and to improve the science labs. And paying proper wages so the best teachers aren't forced into better paying private jobs makes a lot of sense. Experiments with magnet schools, and specialty schools within schools are wonderful in that they offer real choices to families within public schools.