and yet still did very well
“And yet”?
OP, think about this mind set that you are in before you do some damage to your DC’s confidence and self esteem.
You were immensely privileged to go to a private school.
The vast majority of schools results simply reflect the overall cohort. Individual students do as well as their own ability and attitude allows, wherever they are, if they have support from home. Children go to state comprehensives ‘and yet’ do extremely well. You know?
Your disappointment at not getting your top choices is surely to do with ‘losing’ in a competitive process. You have no business competing via your Dc.
Support your child to fulfill their potential, do their best and, most importantly, be happy.
They have done incredibly well anyway to get through numerous competitive processes. Celebrate your child for who they are.
Think about the implications, from your child’s POV, of your sulk!