I am sure you are right annie in saying that to the parents this baby is not dead - I know you have personal experience of similar sad situations, and will know much better than many of us, who thankfully have not suffered in this way.
The parents do indeed need time to come to terms with their decision; but there has to be a moment when the decision is made to let him die - the longer it drags on, the more they will continue to bond with him and the more difficult the grieving process will be. Their emptiness when Charlie is gone will be compounded by a huge change in their life and status in relation to the media, which has filled a big chunk of their lives over the last few months. One cannot but fear for their long-term well-being, and, as I mentioned upthread, they need a counsellor beside them, both now and in the future.
I have seen situations professionally when young adults were saved following an accident, but later found to be brain dead and difficult decisions had to be taken. Unimaginably sad for them all, but I never came across parents who did not accept the prognosis and take the brave decisions needed.
I understand the parents' wish to see Charlie moved from the hospital to hospice care, because their relationship with the staff there has broken down. But that would satisfy a need for them, rather than necessarily being the best thing for Charlie, who will have to suffer the disruption and possible physical distress without any benefit from being elsewhere, as he is insufficiently conscious for it to make any difference to him.
This case does highlight the challenges of modern medicine. Charlie would have peacefully slipped away long ago before medical advances made it possible to keep his body alive with no hint of meaningful human life.