BA paying more than other airlines? A good bit of misinformation that one! Schools with a BA contract will be be making a loss. BA use their size (large fish in small pond) and national flag carrier as bait for the schools.
"You want our contract? We will pay this amount." The school will bleed with every BA student. But they all want to be able to say, "We train BA students." If you are not a BA student you are paying a higher price. Schools have to make up their losses somehow.
I have a dream that one day all the schools will get together and work out a price for BA that is just. A dream I know, the schools will say yes and then do a private deal.