It gets down to 0F here many nights of the year, so 2-3kw of batteries would not nearly cut it. Even with a gas furnace it's pulling 1500 watts when heating so I would need a minimum of 7-8kw of batteries just to get through the night running nothing else.
If I am doing brand new construction I would definitely have a bigger hand in the design of the property and realistically I would have both electrical battery storage and some kind of fossil fuel generator for flexibility during a sustained power outage.
I would love to have a completely off the grid place that still had fast internet speeds, but haven't won the powerball yet so that's not going to happen anytime soon.
Tesla's big contribution to solar really is the power wall since the battery packs are very high end and require little (zero?) maintenance. I know someone who has marine batteries for night time power generation in a mountain cabin, it's a huge PITA because the batteries have to be serviced and periodically replaced. When you put it in and it's all shiny and new and your lights work 24/7 it's pretty awesome, then 15 years later after replacing thousands of dollars of batteries and dealing with the occasional battery that leaked while you were away for a couple of months... not a lot of fun.