Thermostats are best if kept simple. Programmable thermostats are complicated, but can save money. Smart thermostats are less complicated, but expensive.
My power company is Coast Electric EPA in Mississippi and their time of use electric rates are reasonable. The electric rate increases 4x for 2-3 hours per day. It decreases the remaining 21-22 hours per day by 50%. If my peak electricity use does not occur during those peak times, I could save some money. And I bet if I manage my electric use, I could save a lot of money.
A good thermostat helps you save money. So a non-programmable thermostat is not a good enough for time-of-use rate structures. Some thermostats can be programmed by the hour and day of the week. But my summer peaks are from 3pm-6pm whereas my winder peakers are from 6am-8am. So I’d prefer a thermostat which can be programmed for each hour of the day, each day of the year. But a simple “day of week” “time of day” thermostat would work just as well.
Cheapest acceptable – $20 (generic time/day programmable)
Cheapest smart option – $40 (Zwave+).
Cheapest smart wifi option – $90 (Brand Name)
Traditional smart options (Nest, Brand Name) – $150+