Has anyone demonstrated that charter schools actually have better processes? Last time I read up on this, it was a pretty hotly debated topic. If I recall correctly, the big anti-charter argument was that charter schools' improved outcomes were almost entirely explained by some combination of more school days, higher funding, and increased ability to kick out problematic students (e.g. no requirements to handle remedial or special education students, expedited expulsion processes because students are only being "expelled" back to the regular school, etc.).
If I remember right, it's also due to the fact that the type of parent that will spend the money and time to enroll their child in a charter school is much more likely to be the type of parent that takes an active role in their children's education.
There's an argument that a charter school's real advantage is that it attracts a higher proportion of parents who want to push their kids for achievement and have the resources to do it as well.
Charter schools that want to have great metrics select students in ways that public schools don't.