It would be great for emergencies. An ideal state would be one where you could charge this battery and use the power during personal peak times.
Yup. Its rechargeable - conventional gas powered generators need fuel to run.
After the initial investment with the Powerwall, it pays for itself by capturing free sunlight and converting that to electricity.
When you have an emergency, it will simply turn on and run your home.
In remote areas, two or three of these could provide required power needs in the absence of electrical grid service.
Another factor in favor of solar/battery storage is their silence.
During some power failures, a generator will be a dinner bell for hungry predators.