Suppose there is a public school with one thousand students. Then a private school opens and pulls one hundred students from the public school.
What happens to the incumbent public school funding?
Well, the school system will lose the per-pupil state funding so the State saves some money. They may lose some Federal funding and likewise the Feds save money. But the incumbent public school system does not exempt the parents of the now privately educated children from school taxes so that system keeps all the tax money it collects. Yet there are about three fewer classes to maintain.
Now suppose that instead of a private school it is actually a state-sanctioned charter school that opens. How does this change things?
In terms of the amount of money coming into the incumbent public school system there is no difference whatsoever and the workload still goes down by the same amount. For the parents who pull their children out of the incumbent public schools, they see a significant drop in cash outlay for their child's education. They still pay the incumbent's tax for an education they cannot or will not use, but now they send their children to a state-funded school. Of course this means that the State does not reap the financial benefits when parents privately educate their children.
What the Amendment One brouhaha boils down to is quite simple: the incumbent public schools' position is that they have sole and exclusive access to all monies spent by the State on K-12 education. However, it is the State, not these incumbent school systems that bears the burden of the constitutional mandate to provide an adequate education. Anyone who has been paying attention also knows that the existing Georgia public schools are far below adequate.