And any arbitrage is also trivially exploited by the electricity company, who has a much greater financial incentive and scale, so there's really no reason to think that it's going to widen in the future either.
You could exploit it yourself, but only if you have several million to invest, less than that and it isn't worth the bother for the electric company to talk to you. Even at ten million invested you really need to have this is round one in your proposal with the understanding you intend to invest a lot more when it proves in the real world to work like you expect.
Until grid-scale batteries are more established, you're helping the electric company, and that's why they're exposing the arbitrage. They're providing the incentives to nudge demand, so a home battery is doing exactly what they want (use more at time X, use less at time Y). Otherwise they'd just have the 24/7 price be whatever it currently costs when the supply and demand curves are tightest for them (when demand is highest and/or supply is lowest).