Behavior matters but smart loads are IMO essential. E.g. we have a tanked water heater that shuts off during peak rates; no way we could accomplish that by hand every day. It's not hard to imagine from there, cars that monitor the 'net and strategize to reach X% state of charge by 9AM with the lowest total cost, or washing machines that wait for the price per kWh to hit some bar before they start running. (although frankly the direct power draw of a washing machine is almost nothing, it's all in the hot water)

We're already getting there a bit with smart thermostats for A/C. Refrigerators might be more difficult, although similar temporary demand response schemes could probably be made to work, e.g. every fridge is alerted to shut off in 30 minutes for 15 minutes, they all schedule cooling in advance, and then drop off the charts as a group for a short window of time. Perhaps you saw that a bank of clouds was about to roll over your panels.

Silent loads like your fridge make up a lot of the total power draw, and are also some of the most tied to the concept of permanent base load.