If there is one thing that the case of Alfie Evans certainly will not do, then it is to instil in the British any doubts whatever about the National Health Service in principle. Americans and others who imagine that this or anything else might ever have that effect simply do not understand what it is to be British.
If anything, the political response to this case will be the call for more money for the NHS, which is consistently by far the most popular institution in the United Kingdom, and which has been so throughout almost the whole of living memory. People who do not like it just do not like Britain. That is probably why they almost always do not live here.