Again no.
"The Italian hospital had acknowledged it could not find a cure, but had proposed maintaining Alfie’s life for about two weeks while doctors tried to investigate his condition."
There are no treatments - even that seems to be agreed.
> In a private healthcare system, the parents would be free to pursue that
If they could afford to write a blank cheque for open ended life support. Any insurance would defer to the consensus of medical opinion and cease treatment. They would have ceased cover long before the 2 year trail of court cases and appeals all the way up to rejection from the European Court of Human Rights (not part of the EU or UK govt).
https://www.judiciary.gov.uk/judgments/thomas-evans-v-alder-...
Given this new evidence, I change my opinion on this: the state-run healthcare did offer the best advice.
(The question of state-run medical systems restricting freedom still applies here, even though the freedom would simply have been different end-of-life care.)
The UK doctors punted, agreed. But Italian doctors believed different treatments were warranted. The Italian government gave the boy citizenship.
In a private healthcare system, the parents would be free to pursue that. But in the state-run system of the UK, there was no such freedom. Alfie Evans died last Monday.