In Mormon theology, why didn't John the Baptist baptize Joseph Smith?

In May 1829, Joseph Smith and Oliver Cowdery went into the woods to pray because of some questions they had about baptism. As recorded by Joseph Smith, they were visited by John the Baptist, who gave them the Aaronic Priesthood. The Aaronic Priesthood included the authority to baptize. John then directed them to baptize each other. First, Joseph baptized Oliver, then, Oliver baptized Joseph. This is an unusual arrangement because baptism generally precedes receiving the priesthood, and usually the baptizer has already been baptized. As I understand it, in order to perform a priesthood ordinance it is necessary to have a physical body (this is why baptisms for the dead are performed by the living by proxy). As a resurrected being, John the Baptist had a physical body – evidenced by the fact that he laid his hands on their heads when he gave them the Aaronic Priesthood. So, he should have been able to baptize them as well. My question is this: Why didn't John baptize Joseph and Oliver, or at least Joseph, and then give him/them the priesthood? It seems that this would better establish the order of baptism first, then receiving the priesthood. Is it something to do with the nature of resurrected beings? Or, is there something specific Joseph and Oliver needed to learn? Joseph Smith's account is recorded in Joseph Smith—History .