Child's Play 1 takes no single point of view, but since we hear Andy talking to Chucky but are not allowed to see Chucky talk for ourselves, I believe that it operates mostly from the point of view of Andy's Mother. It's through her we get the doll, through her that the fact that the doll is alive is finally confirmed. One of the fears it works on is that something out there is corrupting your kid. You get home, your best friend who was babysitting him has been murdered, and he's so deep inside his fantasy world of his "Good Guy" doll that he doesn't even care, it isn't real to him. You have to always be there for him, but at the same time you have to teach him how to properly control his imagination. It's a distressing situation.
But Child's Play 2 is the only film that really works on what is probably the scariest possible angle using this premise: You're a kid, powerless, and no one believes you or cares to help you. Andy's frustrated, frightened, there's a killer after him and his mother is unavailable because she's been locked away. I almost feel like he should have been adolescent in this one, as opposed to part 3, to better work these themes of aggression, frustration and having to grow up and stand up for himself. The film itself is not great, but I think it keeps the story moving and it raises the stakes fairly well, making Andy's world crumble around him more and more.
The only reason I don't like it as much as part 1 is because I love the aspect of the first Child's Play that this Voodoo strangler asshole has been forced into the body of this fucking little doll. A common complaint is that, at the end of the day, a doll is not intimidating. The best part about Chucky in part 1 is that he KNOWS this and he HATES it. He can't even wrap his hands around people's throats anymore! Instead, he is forced to sneak around and make do killing whichever way he can, whether it be surprising you so you fall out a window or stabbing a voodoo doll of yourself you keep around the house (by the way, why the fuck would you do that?). Part of the reason he's such a bastard is because his present condition makes him cranky. Every other entry, he seems to enjoy being a killer doll too much.
Also, in every other entry, he's too much of a character, which diminishes the effectiveness of the puppeteering. In Child's Play, he really only has that scene with the Voodoo priest where he's in full view, walking around and talking, the rest is achieved through very good editing and a wide variety of puppeteering techniques.
Now this long post may lead you to think I consider the films to be classics, or even good. Not the case. Most of the films amount to an interesting waste of potential, most the time. Still, there IS a reason that he continues to freak little kids out after all these years.