"But they still have rainy weeks where they run out of power and have to run their gas-powered generator to keep the refrigerator from spoiling."
You don't need to run any other appliances all night when the sun isn't shining. Also, why would you even have a microwave, toaster, and ELECTRIC dryer? Those all use obscene amounts of power.
I live off-grid and we run laptops (using boost converters) and lights directly off 12v DC. A big part of making an off-grid system work is reducing your consumption drastically in ways that you can't even do if you're plugged into the grid.