Why should they have access to my tax dollars if they are privately educating their own children?
Also, most parents would be sorely disappointed in the pittance that is given to the schools to educate the children. Also, using my numbers for my property taxes and money given per student to the high school where I was the assistant principal, if states just refund the tax dollars contributed by the parents who home school, you will get about 1/4 of the costs needed to educate a single public school student.
School finance is complicated. In fact it is a semester-long course in graduate school and was a struggle for my mathematically challenged colleagues.