What I don't understand, and what probably hasn't helped the family come to any acceptance, is why it's been reported on in a such a "neutral" (struggling to find the right word here) fashion in the media?
Archie is regularly referred to as "brain damaged" or in a "coma" - massively minimising the fact he is brain stem dead. Hollie is quoted as saying he will recover, there are therapies that could help, he's going to be euthanised/murdered etc, without any pushback from interviewers or corrections in articles.
If I was someone who knew nothing about the case, I would also think he should have more time, based on this alone.