The answer to this question is clearly indicated when George, out of desperation at trying to understand his children and their worrying attachment to the nursery, brings in McClean, the psychologist, to show them the nursery and to discuss his children with him. McClean gives George his analysis of the situation in the following quote that clearly signposts why the nursery is so important to the children:
Where before they had a Santa Claus now they have a Scrooge. Children prefer Santas. You've let this room and this house replace you and your wife in your children's affections. This room is their mother and father, far more important in their lives than their real parents. And now you come along and wnat to shut it off. No wonder there's hatred here.
George and his wife, by being "good" parents and buying their children this nursery that is more real than reality itself, have allowed the nursery to become more of a parental figure than they themselves. Bradbury therefore uses this story to paint a worrying and disturbing image of what our future could look like if we allow technology to displace normal systems of human relationships.