Heat is the #1 reason people run the pump on a timer.
Theoretically aeroponics will provide enough o2 to the roots, that they should not need a "drying out" time, like as is required with soil or ebb and flow hydroponics.
However, it seems that the problem isn't the lack of o2, but the fact that when roots are soaked consistently, they tend to mat together. When the roots are fluffy and spread out, they grow many tiny little white hairs that are very effective at absorbing water, nutes and o2. When they become matted, you will see less of these fine root hairs and the plants will not grow as fast.
So, the #2 reason would be to allow the roots time to dry out, not to provide o2 in and of itself, but to allow the roots to "fluff up" again(which they will not do if being sprayed constantly).
