I'm not talking load so much as network traffic. Companies like Amazon and Google have huge peak hour outbound traffic during US waking hours, and then a huge dip during off hours. If they can push more of the traffic into those off hours they can make the marginal cost of the bandwidth basically zero.
So if you make a request at peak hours (say 12 noon ET), they just make you wait until 11 PM ET to start downloading, shifting all that bandwidth off their peak.
Even if you're just "flattening" the peak, when it comes to both CPU and bandwidth, that's a major cost reduction since their cost is driven by peak usage and not average usage in most cases.