What you've expressed is a contradiction in terms. You can't have true, full *local* control of schools and have "choice" at the same time. True local control means that you have a local school board that answers to no one except the state department of education. It means that the *only* students who may go to your district are those who live within the district. Further, in its most ideal form, it means that the *only* local elementary school your kids can attend is the one nearest their home. There would be no bussing into the district, and no bussing within the district, for "racial and economic balance" or anything else. People who bought a house in a particular area would be *guaranteed* that their children would go to the local school.
The local district would be accountable to the state (i.e. making sure it kept adherence to the state laws & regulations), the local school board, and the voters. The federal gov't, as you put it, should have *no* input into education whatever.
If one's school is based on where the family lives, then "choice" comes in by the ability to move wherever you wish. But if education is truly local, once you live in a certain house, your public-schooled children will go to the *local* school.
"You can't have "full local" control of schools and have "choice" at the same time."
Why not? Local control of the schools does not prohibit bussing across town to a better school where I live. The school board is elected locally. Though there may be state regulations, at least the state is closer than the federal government, thus more reachable. (Local meaning
city, town, or country.)