The 'living off the grid' angle is a red herring. The main application of this would be solving the peak load problem, ie smoothing out the load on power stations throughout the day. It is not clear to me how a LiPo batter is better suited for this than other battery types though, especially since weight is not a concern for a stationary battery in your home.
I wonder if this even needs to be something in the home. Wouldn't it also make sense to install these things, in bulk, in a place where they could service several homes? Say, at the block level. If it is part of power distribution infrastructure as opposed to a consumer product, then that simplifies some of the safety and maintenance issues; concerns like weight or volume are even less important if they are housed in a dedicated structure.
Isn't part of the problem that production costs for batteries are so high? I suspect this is Tesla staking claim in a market that will grow as the price of large rechargeable batteries drops. And that price drop will in large part be due to Tesla.