This is a situation that will be so very hard for the parents to understand. If Alfie is only in a 'semi' vegetative state (what an awful term, I wish we could find a more pleasant one), then he will be moving, and seeming to respond to stimuli. It will be very hard for his parents to understand that those responses are random and not linked to what they are doing.
He's their boy. He's so little. I think it's very different if an adult becomes like this. Relatives can reason it out. "This isn't Terry. He would hate to be like this. He wouldn't want to live his life just hooked up to a machine, not able to do anything or move anything, etc."
But he's a little baby. He's just sleeping on their lap. Babies do sleep on your lap when they nap. They don't have hugely established personalities that we can refer to and say "this isn't x". We're designed to cuddle and protect babies and young children.
The doctors will be working hard, and they'll be frustrated that they don't know why he's so ill. But court is the right place for the decision to be made.