Why is it necessary to believe in a human Messsiah? Why not simply look forward to a Messianic age when the world will be perfectly G-dly?
If G-d desired to usher in the Messianic era Himself, why did He bother creating us in the first place?
Throughout history, G-d has chosen human messengers to make His word known to mankind. One reason why G-d chooses human agents is that the whole purpose of creation is to synthesize the physical and spiritual domains.
The leaders of the Jewish people in every generation serve as prime examples of how to live a G-dly life, within the bounds of the physical universe. They also give energy and direction to the entire Jewish people to enable them also to reach this level. The tzadik serves as a bridge between the physical and spiritual worlds; better put, he shows us that there is no dichotomy in the first place.
Exile is a state of mind, in which there exists a barrier to the aforementioned synthesis between the physical and spiritual. To lead an entire nation out of exile requires a person who lives within the physical world, acutely aware of world issues and problems, and who simultaneously is in touch with the G-dly. In every mundane thing he sees divinity, and he shows us how to elevate it to its ultimate G-dly purpose.
To believe that G-d will unilaterally change the world without human involvement is to deny our role in creation as G-d's partners. If G-d desired to usher in the Messianic era Himself, He could certainly do so; however, if so, why did He bother creating us in the first place? Thus, the most rational approach is that G-d will change the world by way of His chosen human messenger, Moshiach, who will lead the world to a Messianic age.