However, I think children that have been brought up in a economically very comfortable stable backgrounds with Prep schools from 4 -11 have a unsigned written contract. This, to at least achieve academically in similarity to their peer group they have been placed with. This especially being true if no issues such as physical or mental disabilities have presented themselves.
This is a terrible concept. They are a child, who had no say where they are placed at 4 years of age. It wasn't a choice for them, you decided to place them there, that's on you OP.
Your children have a responsibility to themselves to do the best they can, not a responsibility or 'contract' with you. Motivation has to be intrinsic to truly succeed.
As I tell my daughter when she moans about doing her 11+ homework, its her choice and her consequences, it doesnt actually affect me, she doesn't have an responsibility to me to do anything beyond treat me respectfully. She has to make a choice for herself if she wants to go to Grammar and to put the work in to get there.
It does sound as though Grammar probably isn't the right setting for your daughter, and that the pressure had squashed her confidence.
As parents we can provide the best conditions for success, such as emotional support, a quiet place to study etc, but we cannot chose it for them, or ask it from them.
My parents regularly moan that they paid for private school for my brother and he is now working in a minimum wage job. But I tell them that was a choice they made, with all the best intentions, but still their choice.