[AnthonyMouse]

> The recipient doesn't necessarily know ahead of time how profitable the investment will be.

Neither does the government.

> Risk aversion will cause them to avoid investments that are profitable in expectation if they believe the chance of ending up worse off is too high.

Risk aversion works both ways. The risk of not making the investment is that electricity prices in the evening get too high and then you have to pay them. If you install the batteries then you have a known fixed loan payment. If you don't you have an unpredictable variable electric bill. Which one triggers more risk aversion?

> By offering interest-free loans, the government can pool that risk

Risk pools don't work for correlated risk. The primary financial risk is that too many people install batteries -- which subsidies make more likely -- causing the price differential between various times of day to become too small to justify the investment. And that can happen even with interest subsidies. So then you have the government expending tax money to not just cause the people who would have installed them anyway to end up underwater, but to increase the number of such people.