These priests and their vestments weren't the end goal; they were pointing to something and someone greater.
The entire Levitical priesthood, including their special clothing, served as a powerful 'type' or foreshadowing of Jesus Christ.
Christ, the True Priest
Unlike the earthly priests who had to repeatedly offer sacrifices for their own sins and the people's, Jesus is the perfect, eternal High Priest. He offered Himself as the ultimate sacrifice, once for all.
Unity of Priesthood and Sacrifice
While the Old Testament separated the role of priest from king, Jesus perfectly embodies both. He is our King and our Priest, bridging the gap between God and humanity in a way the earthly system could only symbolize.