Let's say you use 1 kW on average in your house. You'll need about 4 kWp of panels to supply that with a typical capacity factor of 25%—a bit more panels than that if you're in Scotland, a bit less in Perú, but about that. At current prices that's US$800 of low-cost panels.

Now consider a couple of alternatives. You can overprovision the panels by a factor of 5 so that even on cloudy days that block 80% of the light, you can continue rocking your one-kilowatt lifestyle. This costs an extra US$3200 of panels. Or you can buy, say, a week of lithium-ion batteries; say you're paying US$150/kWh for the batteries, which is in the ballpark but not exact. You need 7*24 = 168 hours of batteries, which at one kilowatt is 168 kWh. This costs US$25000. In both cases you need some power electronics (charge controllers, inverters, etc.) but this is not a significant cost difference between the two scenarios.

So 5x overprovisioning of solar panels costs you about an eighth of a week’s worth of battery storage. You can overprovision by a factor of 50 for less than the cost of that week-long battery backup. There's a trade-off between the two—more battery storage means you can get by with less panels, and vice versa—but this strongly suggests that in most cases the optimal trade-off is not going to involve multi-day battery banks.

How about a few years in the future? This year, panel manufacturers have apparently sewn up the market in a cartel, preventing prices from falling over the last few months. But sooner or later, the cartel will break down, and panel prices will return to their long-term learning curve, say 20% per year until the raw material costs dominate. In 5 years, panel costs would then be 40% of what they are today: 8¢ per peak watt instead of 19¢. No such dramatic cost reductions are on the horizon for batteries.

But in a lot of cases, shifting demand to times with cheap energy is still going to be cheaper.