High school isn't free. Someone is paying for it, it doesn't operate on good will and fairy dust. That someone is taxpayers and in many jurisdictions the avg. tax bill is $7-12K. Also in many jurisdictions what is called "public school" is more like nursery school with 50%+ of graduating students not qualified to go on to college. In those areas a lot of parents do opt for private high school which can cost as much as some colleges.
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How smart is the registration algorithm. Think it would be fooled by alumni.edu?