All school choice does is give poor parents the same kind of school choice that rich parents have.

If you're rich and the schools around you suck, you just move to a neighborhood with good schools! That means you pay taxes in that school district, which fund your kids schools.

If you're poor and the schools around you suck, you have no choices. You send your kids to the sucky school.

School choice would mean allowing the same choice for poor folks. They would be able to choose where their kids go to school, and their tax money (in the form of a voucher) would follow them to that school.

How could such a scheme "retard public education efforts"? The point of public education is not to prop up failing state-run schools, the point is educating the public. Undermining shitty schools is a feature, not a bug.