That video's conclusion is misleading - he's only shifting his fridge's energy consumption. That's not actually much in the grand scheme of things - it's a well-insulated box that is already a thermal battery. In fact, he only discharged his power bank to 64% at the end of the day, so he didn't even use up his full capacity (that he paid for and is factored in his spreadsheet).

Batteries can provide significant savings but for that you need to actually use them fully, either by load-shifting significant loads (if you have enough to fully consume the battery capacity), or just charging/discharging the battery directly into the grid (essentially acting like a grid storage system - charging the battery to full when energy is the cheapest, and dumping it back when it's the most profitable). Even better when you have solar - instead of selling that energy at low feed-in prices, save it in batteries and use it once the sun goes down so (if you have enough battery capacity) you never ever need to actually "buy" any energy from the grid.

I believe the Pila can technically do the above, although its battery capacity is probably too small to ever recoup its purchase price on this type of arbitrage. However, the underlying concept is absolutely workable and profitable with the right equipment.