If what you say is true, then with better economies of scale and longer investment horizons, utilities would quickly erase any peak-vs-non-peak arbitrage opportunities.
Consider the power output characteristics of some common energy sources:
Gas, Nuclear, Hydro, Wind, Solar
Our "sustainable" sources of power - hydro, wind, and solar - are also the ones with the most irregular and unpredictable power output. This creates a problem, because even if there was enough cumulative power output from sustainable sources today, it most likely wouldn't align with our usage schedule.
So there are two solutions: 1) find a way to map the sustainable power output to our usage 2) find a way to store energy
Today, our most readily available form of energy storage is gas. We just put it in a container and burn it when we need to. "Spin it up," if you will.
An alternative to gas is a crazy network of Powerwalls. The hope is that, eventually, instead of spinning up gas turbines during peak demand, we can just draw from our Powerwall.
There was another alternative on HN recently. Basically a super-deep hole in the ground with super heavy object falling into it, but suspended by a rope. You run a motor to lift the object during off-peak hours, then let it fall and spin a generator during peak hours. I can't find it right now but I remember thinking they had a great name.
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That said, power output is only part of the problem. If you're looking to factor the potential disappearance of arbitrage opportunities into your buying decision, you also need to consider the time until regulatory changes allow for perfect pricing, and the time until these Powerwalls have precise enough information to decide exactly when to draw from the grid versus the battery.
tl;dr: "quickly" is probably optimistic. We're a long ways away from economies of scale.
Or a train going up and down a hill...
http://www.aresnorthamerica.com/
Both are basically the same concept as pumped hydro which has been in use for a long time... pump water up a hill when energy is cheap, let it fall down and turn a turbine when energy is expensive. And hey, if it rains, free energy!
The rail/hole in the ground approach have the advantage of taking up less land I suppose, but I suspect are less efficient.
Now, vanadium-redox flow batteries... That's always been my pet large-scale energy storage. That or hydro.
However, there is a bunch of companies that buy and sell electricity on the open market, so they have a direct financial interest to play with this arbitrage.
In the UK, another reader has calculated the best case scenario was profitability in about 10 years. (his numbers ring true to me, I calculated recently that there was no reason to take an economy 7 contract for my electricity usage using similar data) That's a lot of time even in the utility market. So if batteries not attached to solar panel are going to be profitable (in the UK), that would be a future generation.
Probably right around the same time they're no longer necessary, as the cost of distribute solar continues to plummet. Its actually truly amazing how quickly the price continues to drop for panels each year.
Considering the rate at which solar power is getting cheaper, I'd say a solar power based economy is within reach.
Chart here: Check out monthly/weekly energy production for 2014 https://www.energy-charts.de/energy.htm