Yeah that stove is what I was thinking of!

And good point on training. I don't know what use cases would be supported by a battery, but there's a marketable one I am sure we will hear about it.

Batteries and capacitors would serve different functions. Capacitors primarily isolate each individual chip and subsystem on a PCB from high frequency power fluctuations when digital circuits switch or larger loads turn on or off. You would still need to use capacitors for that. The purpose of the batteries would be to support high loads on the order of minutes that exceed the actual wall plug capacity to deliver electricity. I am thinking specifically of the stove linked in your sibling comment, which uses lithium batteries to provide sustained bursts of power to boil a pot of water in tens of seconds without exceeding the power ratings of the wall plug.