Lead acid batteries cost about $100/kWh nameplate. But at 100% depth of discharge they wear out VERY quickly. We'll assume 50%. That means they cost $200/kWh in actual capacity.

At 50% depth of discharge a lead acid battery will only get about 1000 cycles before it's not very useful anymore and needs to be replaced.

$200 / 1000 cycles = $0.20 per kWh per cycle.

That's the fixed cost of a lead acid battery. Every time you charge and discharge it, you've lost $0.20 per kWh in terms of the capital cost of the battery. This has nothing to do with the price of power, but it has to do with the depreciation of the asset.

Okay so now let's deal with power cost. It's 14p to buy low, 19p to sell high. Since I'm in the US I'm going to convert that to dollars at the rate of about 1.5 which means that the MOST money you can hope to make on the arbitrage of low price to high price is $0.06

Now let us compare $0.20 per cycle of cost with $0.06 per cycle of revenue (again ignoring the fact that in reality nothing is 100% efficient) and we can easily see that this is a losing proposition. It'll lose AT LEAST $0.14 per kWh per cycle for the person trying to operate this arbitrage scheme as a business and they'll soon go bankrupt. Problem solved.

Now if the cheap power was $0.01 and the expensive power was $0.50 then they might be able to make money. But from what I understand of the power pricing, that's not the case.

If you'd like to continue to argue, please do so with actual numbers that mean something and/or are based on reality, rather than belligerent trolling. Please see this link where I previously did the analysis that you couldn't be bothered to read: https://news.ycombinator.com/item?id=9063702