Either way, that’s a separate issue from national healthcare, and it’s something that’s going to be an issue no matter what.
The general idea is to prevent parents from actively harming their children with untested treatments - just like the courts can force parents to provide necessary medical treatment, they can prevent parents from applying medical treatment likely to cause serious harm. Whether Charlie Guard was an overstep is definitely a live question - I’m inclined to think it was. It’s just one that’s going to be there no matter how we manage healthcare.
(The Supreme Court thing is because it was in the UK, not in the US, so the system is a bit different. It would be a state issue here.)