The scenario that you've described simply doesn't exist for the vast majority of Americans. It's in the realm of vouchers; not too bad of an idea in the theoretical sense, but not likely to be seen in reality.
You work with the tools you actually have. For the vast bulk of Americans means home education, private schools, or settling for the government schools.
"The scenario that you've described simply doesn't exist for the vast majority of Americans."
Jedem das Seine. Not everyone needs it, and not everyone would be able to benefit from it, either. A somewhat similar scenario existed in American public schools about 100 years ago - witness all periodically re-published exam requirements for the high school entrance of that time. And the entrance exams imply the same selectivity - not everyone was admitted.