I think another factor is that the brain damage cannot be reversed. So even if he survived, little Charlie would be blind, deaf and completely paralysed. And suffering seizures every day. One wonders what sort of 'life' that would be...

My poor sister, a doctor, had to make a terrible decision regarding her young husband of 36. She had two young babies when he collapsed from a massive brain aneurysm. He was kept alive on a ventilator, but was virtually brain-dead. She bravely agreed that the life-support should be switched off and as many organs as possible taken for transplants.
Her decision saved the life of many people, but it was a dreadful time for us all.
These situations are never easy and I pity Charlie's parents with all my heart.
I think perhaps the US doctor should be allowed to try, but then the Court should rule in favour of GOSH.
At least then the couple would feel they'd done all they could.
(Not that my feeble opinion carries any weight at all, and it would be arrogant to maintain otherwise)