People already DO react to time of use pricing and it is in use in many places round the world at retail level and most places at commercial and industrial level.
One thing to note at the retail level is that typically not even the majority of the retail cost of a unit of electricity is the energy itself; infrastructure costs and so on are folded in too, so the price swings are a lot less dramatic than at the wholesale (or balancing) level which can range from 3:1 to 10:1 in the GB market for example.
The GB's best-known ToU retail tariff (sadly we don't have a national real-time one) is Economy 7, designed originally to soak up power at night from nukes that couldn't be turned down. (It's not only renewables that have stubborn timing problems.) I think the unit price ratio is about 3:1 between day and night. One third of domestic electricity use is on that or closely related tariffs, or 10% of all GB electricity consumption roughly. (The definitive source of this data is DUKES https://www.gov.uk/government/...