She has control over student loans, educational funding, Title IX statuses, a lot of power for someone who treated the public school system with disdain, and with no experience AT ALL.
Don't agree with her appointment at all.
However her disdain for public schooling system has no bearing on anything. Fallacy that it should.
You don't have to like the work a department has traditionally done to be good at kicking ass and making sure it's run correctly. It could be argued honestly that the reverse is true.