Voters like to be presented with multiple points of view. It helps them evaluate their stances on political issues and reassure themselves that they are making the right decisions when they go to the voting booths. A one-party political system does not present multiple viewpoints and would soon spawn another party as a result of voter dissatisfaction.
Most voters do seek a divided government because they have a strong commitment to their political party. This loyalty or identification with one's political party can be very long term. Although those who are independent voters do not seek a divided government, it is still more popular because there are more democrats and republicans than independents.