That's an overemphasized problem. There's a lot more space to cheaply time-shift electricity demand (i.e. not with batteries) in response to variable pricing than most people realize.
Once we get enough solar installed that it is powering most of the air conditioning when it's most used (which, contrary to what some are saying, is close enough to grid parity to be inevitable in many places), time shifting will be much less advantageous.
At some point, storage is going to play a huge role (there are places where it's already starting to, like Hawaii). It's frustrating that we're still having so much trouble bringing down cost per kWh, but with all the disparate technologies being researched, I think it will happen eventually. Just not as soon as some of us would have liked.
It's not effective right now because we have a grid built upon the assumption that demand and supply are relatively static.
Ultimately the latter is better, but there is so much nuance involved that I don't expect it any time soon. I personally believe that anyone interested in pushing the true efficiency envelope should be looking at getting the most out of off-grid systems right now, at least until more promising innovations show up within the grid itself.
Isn't that still a big win in the short term? If half the world's daytime electricity came from solar, we'd be in much better shape.
Next, there are many ways to store energy. Desalination is a great example where they need high pressure water so just pump it up a hill in the day and all you need to 'add' is slightly more pumps and a large pond. Heating and cooling are another area where storing the output tends to be very cheap.
Finally, people just need less energy when they sleep. Your work PC is probably also asleep for example.