These products do exist, and while the price is still high I do like the idea. Then you can do high power cooking with a more modest electrical draw, because the stove draws high power from its local batteries and charges them more slowly via a wall outlet. This allows installation even when high power wiring is not available.

Induction cooktops generally require 220-40 outlets, so I get that a battery might be a way around that, I doubt it would work for code however.

A household battery made out of old Tesla batteries sounds like a good idea, but I think someone has thought of it.

If those batteries are too old/weak to effectively power a car how useful are they going to be at powering a household stove?

Especially when why would you need such a thing anyway when you have 220v+ just itching to get the job done directly from the grid? The grid needs power storage, yes, but there's all sorts of solutions to that beyond lithium ion batteries including water & stone gravity storage systems. Or just centralized batteries.

That really isn’t how it works. They hold less charge, but you can have more of them and weight isn’t really an issue. They can also charge more gradually, making the dynamics really different.

A battery bank at home can be a good solution to grid balancing, eg if power is cheaper during the day or night, or if you have solar. Water storage systems aren’t very efficient and need lots of space, but there are people who do it. You can also compress air into a cave. Batteries are just something that are cheaper and more space efficient than other solutions.

Centralized batteries work as well, though they don’t do anything if you have lots of grid failures.

A battery bank at your house and that same battery bank at the power station are effectively equivalent. There's no benefit to distributing batteries here since transmission costs are relatively small.

So while yes water storage systems need lots of space, that's really only a problem if you're trying to distribute it. But you don't need to, you can centralize power storage to alleviate time of day spikes. Which many power grids already do.