"...when there's a huge peak in electricity demand at 6 pm when everyone gets home?"

The entire electrical generation industry knows all this. They know when clouds are coming and when wind will stop and model it all. Pricing information is sent ahead of time and plants know if they will be required to spin up or spin down well in advance. Especially something as simple as "everyone gets home at 6pm at a regular time every weekday". It is easy for plants with slow ramp times, such as nuclear and coal, to plan for that.