Hold your horses!
Firstly, there is scientific evidence anorexia is not caused by schools. I'll come back to that.
Although they don't know for sure what causes anorexia, there is a clear pattern of combined factors which contribute to it: 1: genetic link...If you think through all of your and your DD's father's extended families, is there or has there been anyone who has had/got any type of eating disordered behaviours?
2: research by experts (Dick Swaab and others) has priproved that this is a disorder of the cecentral cortex and the hyperthalmus of the brain. Swaab puts forward the credible theory that children with anorexia were starved of oxygen briefly at birth, which had no detectable affect at the time but upset the chemical and hormonal balance in the brain and this sets off a chain reaction when hormonal changes occur in puberty. His studies show that for a large % of children, this could have been a factor. (Brain scans have proved he is right about the hyperthalmus.
So, what happens when these hormonal and chemical imbalances are triggered? It affects the parts of the brain which control body image, the need to drive oneself to perfectioniam and the desire for starvation/loss of appetite. There also seems to be a lack of boundaries concerning care for others (they put others before themselves to the point of putting themselves at risk).
So going back to school; what you are seeing is the illness in control, driving your DD to perfection and high grades. This is not the school's fault or hers.
Before you think of taking her out of achool, listen to what her care team have to say.
For us, the treatment involves family based therapy as I've outlined above. If my DD does not eat her breakfast, she cannot go to school that day. That is the only reason she eats it. If she does not eat up all her lunch, she cannot go back into school. Again, that is the only thing getting her to eat. Playing off one part of the illness against the other is best way to combat it.
I have suggested that DD drops one of her subjects (she's heading for A/A* in thwm all) but she refuses. We're going to wait it out and see if next year she might like to.