I used to work for one of the Electric Co-ops. The reason they want you to conserve energy is simply money. The total cost of electricity to distribution co-op is based on both demand and usage. The rates to co-op consumers don't fluctuate with actual cost so the incentive is to keep cost down by shaving peak demand.
Wholesale power providers do experience higher costs to meet peak demands. Have to fire up gas turbines, use available hydro and in the olden days even old repurposed submarine diesel fired generators. And peak demands require them to keep their reserve generation capacity ready to go which costs money, and operating costs for peak generating capacity is usually quite a bit higher than operating costs for base generation capacity. So in the end, it makes sense and it's really only fair.