You are going to build panels that will provide enough energy for one day on the day it is the least sunny at the site? What do you do with the excess on sunny days?
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.