That is not really the problem and also not totally factual. This is how SOME schools may work but the system is not uniform and, more importantly, enrollment is but a single factor in the calculation for those that do. If a school had zero students it would still receive some funds through the funding formula at any district as far as I am aware. Well, at least if the district allowed it go that far as we know they would have consolidated it long before the number hit zero. So no, the tax dollars for the student really are not gone.
Another factor is that those tax dollars are still sent to the state. The issue with school choice is that we all have to pay for public schools and then you are demanding that parents pay AGAIN to send their children to a private one. For the vast majority of people, this places private schools out of reach for them and leaves it only for the wealthier Americans.
Finally, schools are firmly against school choice in general as, afaik, there is not a single district in the entire nation that allows one student from a district in a state to go to another public school district in that very same state. This should be a damn GIVEN, as a member of the public you should have the ability to bring your child to ANY public school that you are capable of getting them to school on ti9me and consistently. Again, this simply fences the poor off from the better schools and ensures that no matter what happens your local school is getting the funds regardless of your students attendance.