The lorebook is where it is mentioned that their poms "change color depending on the flighty creature's current moods." I don't think there's any evidence of that in-game, so it doesn't explain the reason for their poms. I agree with the other poster about how the poms are possibly for attracting mates. When you first interact with a delivery moogle as a new player, they mention "dreaming about some beautiful mooglette with a rainbow colored pom-pom."