As I see it, there are two 'norms' with profit-driven companies. On the one hand, you have an all-out race to the bottom. See TalkTalk, BT, etc.
On the other hand, we all know that private schools tend to be very, very good. We also know that they tend to be very, very expensive.
So for the private sector to enhance our schooling is no doubt possible, but not without working-class parents being asked to stump up amounts of cash that they just don't have.
But there is the possibility that privatisation *without* extra funding will indeed create a race to the bottom with our schools. No extra funding but need to generate profit = lowering standards, not raising them.