As a consumer in Ohio, variable-rate pricing kind of scares me: It's nice to be able to run the clothes dryer without any concern over what time of day it is. We don't do variable-rate pricing here (at least for residential users).
But I'd manage to sort it out in pretty short order, I think: It usually isn't very important to me what time of day the clothes get dried (as long as they don't sit long enough to get stinky), so I would indeed be motivated to pay attention to that. I, myself, would even become motivated to automate it so that the clothes begin drying automatically when energy is [relatively] cheap.
I can also imagine things like automating water heating: Burn Joules when it is cheap to do so, and store [most of] them for later use at a time that may be more convenient to me. (The math gets interesting on this one.)
Having very cheap energy be available occasionally would also be neat: I've got computationally-intensive tasks that need to get done some day. These cost real money to run on the hardware that I have. It sure would be nice if I could save some money by only doing these tasks when power is cheaper. (Right now, I do try to optimize timing them for energy efficiency. For instance, in the summer it is cheaper to run them on cool nights when the windows might be open than during a hot, sunny day when the aircon might barely be keeping up.)
Realistically both things will need to happen. There is a lot of demand that can’t be time shifted by more than a few hours. We need storage for a few weeks of consumption eventually.
Instantaneous pricing for electricity motivates people and industry to make better choices.
Very cheap energy will enable interesting things too.