This is why a major part of the solution is electric vehicles. Why put batteries in a warehouse and then run vehicles on petroleum when you can put batteries in a vehicle, install twice as many renewables because you now have more demand for electricity, and then charge the vehicles when generation is a large percentage of rated capacity and still have enough to run the rest of the grid when it's a smaller percentage?
It will be a mix. There is certainly still a lot which can be done on the demand side, e.g. when to cool a cool storage house during the day, or when to run certain production lines.