(And the kind of optimisation that happens with this kind of paper is really in the margins stuff. It generally helps the predictive power of the grid, and usually doesn't make much money once more than one group starts doing it, since it's pretty cheap to run and the margins shrink quickly)
Why would anyone give them money if they were just going to throw up their hands and go ‘well, nothing we can do I guess!’.
There is of course the risk that the money gets burned instead of more money getting made, which is the risk in risk/reward.
Rent seeking type behavior tends to happen when there are no obvious ‘green field’ type endeavors to invest in. Or when risk appetites are trending negative.
Note - many of those people with money that want to use it to make more money are retirees, pension funds, etc.
i.e. if we want to avoid food shortages, we need to overproduce the raw goods and therefore waste some. Transporting and transforming those raw goods into food that someone can eat still costs money, it's not just so farmers can get paid. We probably should still actually make sure no-one goes hungry, but that does actually involve some cost and effort on the part of the government, and the challenge there is mainly political elements who don't like the idea of someone getting something for free.
Poverty and misery in the world are mainly caused by this kind of mechanism.
On the other hand if prices are high, and someone has sells electricity that was bought when prices were close to zero, then the cold people will get warm for cheaper than if there wasn't a battery.
Sorry, but you really make no sense.
In case of some failure of the system you're proposing, the prices would skyrocket, the poor would not get power at all, and the rich would have power all the time but for a very high price. Economically speaking, that's great for investors in batteries and supporting systems, socially speaking, it's a horible world to live in. And the system is very unstable already, in portugal it already failed horribly not long ago.
What makes this application of this social regime so different from e.g. food or medicine?
In the short term adding more batteries may allow someone to generate income using this strategy but long term what it will do is push electricity prices down and prevent power generation from being overwhelmed. As the battery "market" gets crowded profit margins will fall and everything will reach an equilibrium.
This is a great demonstration of how capitalism works and why it's beneficial.