What really concerns me is that there is clearly not an effective legal system in place to deal with these sorts of scenarios. When there is unequivocal medical evidence that someone is brain stem dead, verified by several independent medical professionals, of course, with agreed upon testing procedures - that should be enough to force the ending of all medical treatment, regardless of the family's beliefs. Why any of this needed to come to court in the first place is beyond me, and doesn't serve anyone's interests.
@EnidSpyton, this came to court initially precisely because Ms Dance wouldn't allow testing to be done. Unfortunately by the time it was done it couldn't be done accurately according to the standard protocols. What we have here is several independent professionals saying Archie is brain dead and has absolutely no chance of recovery, but unfortunately the relevant protocols don't really cater for this situation and none of the professionals are able to say absolutely that he is dead whilst he remains breathing and with a beating heart. That's essentially a medical issue, not a legal one.
So what the legal system does is to work on the basis that he is alive and consider where his best interests lie. That is a very well-established, tried and tested but nevertheless difficult procedure, and inevitably it is going to be something that is much more subjective than just deciding whether someone is factually dead or alive.
If you can come up with a better system, I'm sure governments, courts and doctors all around the world would be delighted to implement it. Over to you.