These batteries aren't going to power your home at night, nor should they as electricity rates at night are dirt cheap (comparatively) when people aren't at work, in factories and in bed sleeping.
These batteries are going to be performing grid marketplace arbitrage and some governments and utilities are providing amazing incentives to do so. (Currently the incentives require the batteries to be tied to solar.)
There are two pieces of your electricity bill (I'm simplifying here) 1) the electricity charge (EC) and 2) the transmission charge (TC). The EC is calculated by how many kWh you use during each (peak/off-peak) period of the day and the TC is calculated by your max grid demand during your largest 15 minutes for the month.
Tesla Batteries are not just about the batteries, the system calculates how to remove kWh demand from peak hours by pulling power from batteries and then recharging during off-peak hours. This covers the EC cost reduction.
To reduce TC costs the system calculates your peak load over the given month and tries to turn it from a "mountain range" (with many peaks) to a "platou". You pay your TC for the tallest mountain for the month. At first the system doesn't know that much about your usage profile and will just focus on the largest peak demand 15 minute intervals. Then over time it will learn more about your usage patterns and slowly platou your grid demand.
At the end of the day it is going to be much more cost effective and efficient to have a distributed grid with thousands of solar arrays and batteries than build out large billion dollar gas fired turbines or even wind turbines.