The PJM capacity market had a big increase in demand response supply circa 2012, though not much of it was from storage. Still, new players are paying attention to these arbitrage opportunities. CAISO is already seeking out corporate partners to participate in demand reduction.
If it was clearly economical, someone like Exelon (who owns nuke plants) would probably be doing it.
Then again, at lest several utilities claims they were going to buy Telsa powerwalls to do it. So maybe the pricing is getting to the point where it's profitable.
Nuclear plants, as you probably know, are almost pure base load solutions. They can't just be scaled up or slowed down arbitrarily. A volatile, arbitrage-based market efficiency would be pretty hard on the existing nuclear base, and could render a lot of plants unprofitable.
Meanwhile, the gas-fired peak load plants are tremendously expensive, because they have so much downtime and are inefficient. One or two decades ago, competing against them with storage was economically impractical. Now, it's becoming feasible. Especially once we start building gigawatts of sitting capacity anyway, in the shape of EV cars.
Large, somewhat unpredictable fluctuations in the cost of generation (solar and wind) should lead to large fluctuations in price of generated electricity, down to minute-by-minute. Ideally, generators want to sell every kwh they can at peak production, even at a lower cost. With modern computer controls, this makes a delightful opportunity for an arbitrage market.
Storage providers - and this could be giants like lake-scale hydro, or dwarves like the batteries in electric cars - could buy electricity from generators when it's cheap, and sell it when it's expensive (the sun isn't shining, the wind isn't blowing, hot day spikes demand, etc). This can be fully automated. Just plug your car into the wall at night. It might decide to buy electricity, or sell electricity, depending on the price at the time. Aggregators could pool capacity across many small providers. Large storage systems could benefit from economies of scale and long-term contracts.
Create a smart grid that can support this, and let the free market solve the pricing problems for us.