>>33478209They are supposed to represent the three sacred treasures of Japan that only the emperor can see (Mesprit is a gem, Azelf is a sword, and Mesprit is a mirror). Not sure what was the thought process that lead to their final designs but I'm willing to believe there is more to them than it may look like.
The pokedex says they shared their traits with humans. Maybe they represent humanity, and their duty to calm Palkia or Dialga down is meant to paralel humans taming Pokemon, since Palkia and Dialga are very beast-like and could represent Pokemon at their most primal.