In this hypothetical scenario, instead of investing so much in batteries, why not just double the size of your solar array so you're not storing 6 months worth of power in batteries? That would only cost ~20K instead of the ~500K for batteries.
The whole winter/summer storage thing is nonsense, nobody sizes a PV system like that.
But if you're going to think like that grid power is also impractical anywhere, since it too could fail. Power is so important that no single source should be relied on anywhere. In inner cities of course your only chance of getting power is the local electricity company hookup, but if that should fail for any extended period of time such a city would rapidly become a place where you could no longer live, especially at latitudes where it tends to get very cold in the winter.
So, nobody (in their right mind, at least) will do a 'pure' photovoltaic system. There will always be some kind of backup-power mechanism, either the grid, a wind-turbine, a battery to tide you over, a pelton wheel fed from a stream, grid power or any combination of the above.
In reality, what most people (today) who want to live off grid end up doing is hybrid-systems. Natural Gas/Propane for heating, cooking, cooling, and Solar for electrical use. (computer, lights)
But then I have seriously big batteries, and am careful with my electricity consumption, especially in winter.
FWIW, I'm living in a cold climate with high rainfall.