One of the issues here could be that it is simply not possible to map our modern ecclesiastical structure into this ancient setting. At the very least king at this time was a religious position (in part). The King was the “anointed one” (language related to Messiah) and from the beginning of his reign we see Solomon involved in temple rituals. Also, we may be in a period with no “dominant” prophet (like Samuel a little earlier or Elijah a little later) but rather multiple or at least several prophets. Thus Solomon may stand as a central religious leader at this point and really may be the natural choice.