Keep in mind that if you're above the 23c-28c tire range for size, fatter tires are slower not faster. The "lower rolling resistance" part is trickily worded "technically true but in effect a lie" thing.

There are 2 reasons that come to mind to use fatter tires:
1. They're more comfortable. They roll over things better, cushier, etc.
2. If you are on a road surface that's rough enough that your tire has trouble keeping traction, then a fatter tire can actually be faster. For example, a genuine dirt road. A skinny tire bounces around and can't keep traction, a fatter one just conforms to road irregularities and rides smoothly over them. I say this from experience - 23c is not a good tire size for Iowan dirt roads.

But on pavement, if you're riding a tire that's fatter than the 23-28c range, a skinnier tire is faster.