Sourcing hydrogen from electricity means splitting water and compressing the hydrogen. The electrolysis step is around 50% efficient, and compressing the hydrogen for storage takes some energy as well. If the light cell is 50% efficient at converting hydrogen to electricity, then your "battery" efficiency is around 25%. A typical lithium battery is 80-90% efficient round trip.
This setup does have the advantage that the cost of increasing storage capacity is relatively cheap. You only need to increase the size of the hydrogen tank. But power output would be limited by the size of the lightcell.
There are other disadvantages besides the poor efficiency. People can't see or smell hydrogen, so you'd also need sensors to detect hydrogen leaks. Depending on how quickly the hydrogen is consumed, you might also have to deal with cold temperatures in some parts of the setup (as ideal gas law means the temperature will decrease as hydrogen flows out of the tank). And hydrogen is a very pernicious molecule. It will leak through metal tanks and pipes. It also tends to make metals brittle. And its flame is almost invisible. Lastly, the lightcell consumes salt, but I'm not sure how much so I don't know how big a reservoir would be or how often it would need to be refilled.
This setup does have the advantage that the cost of increasing storage capacity is relatively cheap. You only need to increase the size of the hydrogen tank. But power output would be limited by the size of the lightcell.
There are other disadvantages besides the poor efficiency. People can't see or smell hydrogen, so you'd also need sensors to detect hydrogen leaks. Depending on how quickly the hydrogen is consumed, you might also have to deal with cold temperatures in some parts of the setup (as ideal gas law means the temperature will decrease as hydrogen flows out of the tank). And hydrogen is a very pernicious molecule. It will leak through metal tanks and pipes. It also tends to make metals brittle. And its flame is almost invisible. Lastly, the lightcell consumes salt, but I'm not sure how much so I don't know how big a reservoir would be or how often it would need to be refilled.