Perrin is a craftsman and his leadership role is the most paternalistic. Rand is the one who defends the world from the Shadow and the Dark One, whose role is constantly fraught with violent & weapon imagery. Just because he's a father in the biological sense does not actually make him the Father, any more than his co-parent is a good fit for the Mother archetype (Maiden and Crone both fit Elayne much better than Mother).

Actually, if we're going by the Norse view of things, Mat might make a better Warrior archetype and Rand as the Trickster, given what a dark and destructive figure Loki could be in mythology.