"She didn't arrive here. She was born here and sustained the injury here."
She may not have arrived here, but her parents did.
And if being born here automatically entitles you to full NHS care, then that will create an incentive for more people to come and have children here.
"Children cannot pay in any way."
No they can't.
But currently the expectation is that their parents have paid in.
Entitlement to free NHS care is based on parents' status.
We can only change that if we make a lot of money available from somewhere.
Where?
Raise taxes? Treat fewer people within current budgets?
"However I do believe that we have a responsibility to children whom we are allowing to remain in our country and who were not brought here with that health need."
As I understand it we were not allowing her to remain in the country until after she had been turned down for surgery.
So it seems that your attempt to narrow the criteria would be unworkable. As would (IANAD) the pre-existing condition restriction.
So we're back to covering all children born or brought here.
"Of 1 million illegal immigrants only a small number will be children with serious health issues which have arisen here and require costly intervention."
I don't think your restrictions are workable.
I think you would have to make free NHS care for all conditions available to the children of all illegal immigrants.
And I think that will be very costly.
Thanks for discussing :)