I think it’s because the evangelists were writing for different audiences and were emphasizing different aspects of Jesus.
Matthew was a Jew writing for a Jewish audience. He is emphasizing that Jesus is the new Moses, the prophesied Messiah of the Hebrew Scriptures. In Matthew 5 when he delivers the Sermon on the Mount, he ascends the mountain and sits down to deliver his sermon, as Moses ascended Mt. Sinai. The scarlet is emphasizing the blood He will shed for the redemption of many (Mt 26:28). It recalls the first Passover in Exodus where the Jews were spared from the final plague by painting their doorposts with the blood (scarlet) of an unblemished lamb.
Mark was writing for an audience of primarily Gentile Christians in Rome who are undergoing persecution, so he is emphasizing that Jesus is lord. Purple is the color of the Imperial power in Rome, so he is emphasizing that Jesus is king even over the emperor and the Roman power. John is writing later than the other evangelists and he is emphasizing that Jesus is God made flesh. The purple robe is emphasizing that Jesus is the real power.
In Luke Jesus is sent to Herod by Pilate and it’s Herod’s soldiers, not the Romans, who mock him and put on him a garment described as “gorgeous” in the RSV and as “white” in the Douay-Rheims (Luke 23:11).
