There is zero chance right now of any battery storage being in the $3/kwh range. Even in the manager-of-the-battery-factory-took-some-home-for-cost situation.
A Tesla battery is roughly 80kWh, and costs $5k - $10k. If it were $3/kWh then it would cost $240. And since most home batteries are 10kWh they would cost $30 (plus electrician labor costs and wiring).