One possible reason that the revolutionary era poets used the meter was to imitate the style

Iambic and the other answer is classical

I believe the correct answer is: They used the iambic meter to imitate the classic style.

At that time, the authentic American lyrical voice was not yet fully established. Pioneers such as Phillis Wheatley (pre-revolutionary era), Philip Freneau, and later Longfellow, all used the iambic meter (among other forms of meter) - first of all, because it is natural to the English language, and second, because they wanted to build on European tradition. Only Whitman would break up with it and establish an authentic American voice.