There's a false dichotomy here.

Local control does not have to imply local funding.

The funding system can migrate to the state level (I find it hard to imagine that the states would agree to an explicit federal level funding system). The control (i.e. how the money gets spent) can remain (substantially) local.

What is objectionable about the current US version of "local based education" is that the funding for it depends to a very large extent on local property taxes. Have the misfortune to be a school student in a poor area, and you will probably get a worse education than someone with the good fortune to be a student in a wealthy area.