High density batteries allows us to have dramatically cheaper electricity. Think of it like this, what happens when electricity is 1/10th the cost? Beyond what others have pointed out (electric airplanes, cars that drive thousands of miles), costs for everything would drop as energy is a core driver of it in every good you consume. If you can pull energy where it's very cheaply available and store/transport it anywhere the world millions of lives would be saved. For example;

If energy is cheaper than the price of water you can pull water out of thin air (dehumidifiers).

If energy is cheaper you can grow food in areas you normally couldn't.

When you can transport anything for cheap you can move food to areas that are vulnerable to food insecurity.

If you can store energy at large scale you can nearly eliminate grid failures, savings lives in the summer and winter.

Costs for transporting food would go down significantly, imagine groceries being 10-15% cheaper.

Assuming airlines have competitive pressure you could expect plane flight costs to drop 20-30% improving everyone's mobility.

Aviation, drones with hours+ flight range, more solar power usage as storage gets easier/cheaper, phones that last more than a day, robots with actually useful battery life, smaller IoT devices. A lot of current tech is severely limited by battery capacity.

Electric long distance passenger planes. Possibly requiring the help of EMALs.

Electric long distance container ships.

Useful portable laser, coil- and rail- guns.

Even longer range drones.

What point is there in gasoline if we can get better energy storage in batteries?