the largest battery farm you can reasonably buy for a residential system.
Really? How large are we talking?
I have 30 kWh on my house, and that easily lasts all night. Even while cooling the house in summer.
In winter I don't get much power from the solar panels, but for about 2/3 of the year my roof can charge the batteries while running the house. I live near Seattle... I'll bet people in California and Texas really could run their homes year-round from solar.
In short, my personal experience disproves your claims.
Now, I am fortunate to be able to afford the large batteries and solar power system... but the price has already been falling and it's expected to fall a lot more. So I am not some 1% elitist. My point is that if my house is as good as it is in gloomy Seattle, there's huge potential in places like California, Texas, India, etc.
Until recently grid-sized batteries were science fiction. Now, Google "Tesla Megapack" and see how many utility companies are buying them.