If you have a way for consumers to bid for zero-price electricity, there are many things that can increase demand now and give reduced demand later when prices are higher. Everyone has a domestic freezer. If the freezer is smart, when prices reach zero, it can switch on and decrease the temperature another 10C. When prices are higher, it won't need to run as it warms up slowly. Similarly with domestic hot water - just run the temperature up another 10C. People are creative: if you given them intermittent free electricity, they'll find a use. The main problem though is that this reduces demand when prices are above zero. While this is good for the environment, it's not good for the electricity industry.
How much money does it cost to build this out to every house, compared to what it saves? And do people want their electricity prices to vary over the day? If you have a lower cost part of the day then you have to charge more the rest of the time, all else equal.
These spot price contracts for end users do exist in many places (don't know about SA specifically). They haven't been particularly popular; I guess most people are scared about the other side of the coin, will I accidentally drain my bank account if I do my laundry when prices are at the roof limit?
It probably works best when you only have some sockets in a home that are on spot price contracts. And on those sockets, you have plugged in a washer/freezer/AC that is smart enough to receive spot price information and turn on and off as prices rise or fall. We're not quite there with all the pieces of the puzzle, but it's all technically possible now and likely much cheaper than using batteries to load-shift.