But also, the expensive thing about batteries is typically the amount of power they can produce. The post used lithium ion batteries as a reference point, and those typically have a power rating between 1 and 4 hours - meaning they can fully discharge an entire summer's worth of stored energy in 4 hours... which is probably not something you need to pay for.
If you want a ton of really cheap long term energy storage, you'd look into a technology more like hydrogen fuel cells. The raw power (for standard home, 10 kW is plenty overkill) is going to be more expensive than lithium, but for storage you just need a bunch of hydrogen stored somewhere safe (probably buried underground in your yard). That's much, much cheaper than lithium ion batteries on a per kWh basis, especially if you are scaling up into the MWh territory.
And, the other big cost saving solution is to just add more panels. It means you'll be overproducing in the summer and you'll have to curtail, but some curtailment in the summer is a lot cheaper than finding a way to ferry all of that energy into the winter. Then you have extra panels in the winter and you don't need as much storage to be fully self sufficient.