Some forms of differential prices based on time are entirely artificial: for instance, telephone companies that charge more for calls made before 6:00pm or 7:00pm. They do this because it is profitable. It lets them charge high prices during the day to business users, while offering cheaper plans to social users later. That being said, there are situations where the economic basis for prices varies considerably depending on time of day (and year). Electricity production is one.
In the future, spikes in electricity demand may be partially mitigated through the combination of variable pricing and smart appliances that can inform users about the costs of operating at different times, or even make autonomous choices to stay within a budget. This video from General Electric provides more information.
While getting rid of daytime minutes would have little real effect on cell phone networks, shifting electricity demand from high-demand to low-demand times could have a significant impact on the electrical system, partly by reducing the need for inefficient ‘peaker’ plants, which top up supply during periods of maximum strain.