I don’t know why I never realized this simple plain thing before today. I was reading the scriptures about shepherds and it hit me. When Christ was born the visitors were representations of himself.

The shepherds came - representing his role as the Good Shepherd. Shepherds are the humble workers whose job it is to serve, take care of and watch over. “There is one God and one shepherd over all the earth” 1 Nephi 13:41.

The wise men (or kings) came with gifts. Christ has all wisdom - the baby Christ was becoming the ultimate wise man bearing gifts of eternal life with God and resurrection. The price or a cost is so high that only he could pay for them. The gifts that others bring of their finest are sacrifices honoring the gift that Jesus was going to give when he died and was resurrected. There are 3, perhaps symbolizing the Father, Son, and Holy Ghost?
No earthly king can compare to heavenly kings. Ultimately Christ will be king on the earth. This is a position of power and leadership in person during the millenium. It’s like the opposite end of the shepherds because kings have glory and possessions, are rulers and have followers. They are worshipped. This is also his role as a judge. He is both the king and the shepherd but started out as the shepherd and will end as king.
Shepherds, wise men, and kings all come to visit Jesus as a baby or child. Each represents the ultimate role of the Savior for us. How I never got this before…interesting read in wikipedia on the nativity…