For grid independence you need to have either multiple redundant sources of energy and a backup generator (which consumes a fossil fuels), an absolutely massive battery (far larger than is economically feasible) or a grid hookup.
I've reduced the energy consumption of our house about as far as it will go without seriously affecting quality of life, and yet it won't go down below 500 W draw on average, so about 10 KWh on a daily basis. On an annual basis we're 7.7MWh surplus but in winter we are net consumers. Starting March 1st we are in the plus on a daily basis and we could - if we had a battery, which we do not - be neutral. But we're still heating with gas and that leaves four months to cover or about 120 days.
During those 120 days we consume 4 times 350 KWh, so 1400 KWh or thereabouts and produce about 700 KWh with the biggest gap near the solstice in December (due to the very short days). It is simply not feasible to bridge that gap with batteries and we also consume about 450 cubic meters of gas per month in that period, which for a house this type and size is actually pretty good.
So I don't buy the 'personal autonomy' argument unless you want to cut your winter consumption to ~30% of your summer consumption, set your house to 14 degree room temperature (in many households that would be grounds for divorce) or get a 500 KWh battery system, which would set you back approximately $300K at the best prices that I can find today. I don't think that's worth it.