If the world will reach its ultimate perfection in the days of Moshiach, why will he need to serve as king?

According to the Torah, the role of king includes two aspects. The first and most basic is to serve the country and meet the needs of the citizens, by ensuring that the government is run properly. As the Mishnah in Avot (3:2) states, "One must pray for the wellbeing of the government, for if not for the fear of it, man would swallow up his neighbor alive."

The second aspect is more lofty and profound. The king occupies a high spiritual stature; he is completely nullified to G-d, and as such, he leads the people to similarly nullify themselves to G-d. Some of the king's spiritual greatness rubs off on the people, so to speak. The awe and respect that they feel towards the king translates into a sense of awe at G-d's own power and majesty.

It is understood from this that even in the days of Moshiach, when the physical world and the body of flesh will be perfected and purged of all evil, there will still be a role for the king to play. Even the greatest scholars and G-d-fearing individuals, through their relationship with the king, can reach a level of attachment to G-d that they could never have reached on their own.

To quote the third Lubavitcher Rebbe, Rabbi Menachem Mendel, the Tzemach Tzedek, "Therefore, Moshiach will be a king over Israel. Even though we will then all be on the level of great Torah scholars, to whom all the secrets of Torah will be revealed, nevertheless, not everything that is revealed to Moshiach will be revealed to them. The level of Moshiach will encompass them, and for this reason he will be king over them, for kingship is a level that is above the intellect of the recipient."

Source: Derech Mitzvosecha, Mitzvas minui melech