Are you really going to get up at 3AM to do laundry? I doubt it.
No of course you are not going to get up at 3AM to do laundry. You would fill the washer at night and it would keep tabs on the electricity rates, running when it gets below a certain price (or when it's getting late and the wash needs to start to get it done before you want to take it out).
Even if you have a timer are you going to leave your wet cloths in the washer till you get up?
Yes. I do that often. I am not sitting there waiting till the washer is finally done. I do something else, like working or sleeping.
You might not remember and those cloths will sit for another ten hours.
That rarely happens and does not harm the clothes. If it would happen often or would harm the clothes I would simply set a calendar item to warn me to get it out.
Are you going to skip your morning shower because it will cost you a dollar extra?
No. I heat my shower water with natural gas. Gas has little storage issues.
If I would use electricity for that and prices would be flexible then I would switch to a water heater with tank that would heat the water when it's cheap to do so, assuming the energy loss due to cooling would not surpass the gains from the time shift.
Another solution is the freezer and the airco. Both can run max at the moment the electricity is required, since both appliances are meant for uses that can handle a couple of degrees delta. Set some limits to them and they would run mostly when the power is cheap.
Electric cars: Most electric cars only need to charge a few hours a night. If you set it so it charges when electricity is cheap then the charging is cheap.
Large users are even more important. Aluminium is a gorgeous metal for it's near infinite ability to be recycled, but initial production requires massive amounts of electricity. A supply following aluminium plant would save a lot.
Same with a water desalination plant.
The other issue with wind power is that it can vary uncontrollably minute by minute. This is the kind of instability that needs to be leveled out by more storage.
That's not another issue. It's exactly the same issue.
Storage does not work (yet). It's simply too much energy in a too impractical form. The load partially following the supply would reduce the need for storage. Not eliminate it, reduce it.