No they can't. That's why Republicans are a big proponent of school vouchers so that parents can choose which school a child can go to, but Democrats say that is racist.

Correct. If you live in [poor high-percentage African-American town in Alabama] you cannot choose to go to high school in [wealthy mostly-white town in Massachusetts].

(Setting aside private schools...)

The commute distance would put a hamper on it even for private schools.

But you can move to a better school district but that requires money.

There are however many areas with decent schools and decent prices which could be a destination. And some minority families do move there.

Some jurisdictions jail parents who send their children to neighboring better districts. https://www.seattletimes.com/nation-world/for-some-parents-s...