DD1 had brogues last year - she would not have worn shoes like the OP's DD even with the hearts. There were quite a few girls in Yr7 who did, though.
This year DD has these but she is an adult 6.5 (also very tall, nearly 5'6'' so a completely different situation). She would not be allowed ballet flats - the school would allow them, I would not.
at a school that will not allow girls to wear trousers, to be honest - would never, ever send my children to a place like that, so completely out of order in the modern world.