I was just being silly. But you want me to be serious again, I think the analogy works for what it was intended to communicate. All analogies break down, but one shouldn't ask an analogy to representative of every detail of that which it illustrates. For it to do that it would no longer be an analogy it would be the actually thing again, including that which is complex and confusing to some and thus defeat the whole point of using an analogy to simply the point.
I think the only point of the barber analogy is to communicate that just as there is a barber even if you see people with bad haircuts, so to the existence of people have unhappy lives does not disprove the existence of God. To make it be a character analysis in which God and the barber are compared is asking of it more than it seeks to illustrate. But, just for the moment I will say that I have known people who have gone to barbers and left looking worse than when they went in, so maybe there is more similarity than you think?