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But that's not how heat works. A larger water tank has a higher volume-to-surface-area ratio. This makes larger tanks more efficient than smaller ones, not less.

This is why elephants need such large ears. Their bodies are otherwise incredibly efficient at retaining heat. Those massive, thin, flappy ears provide them with a way to expose their blood to a much larger surface area of skin.

Your average household uses somewhere between 30 and 60 gallons of hot water a day [0], and a bigger tank will just have water sitting in it, going cold. Any extra surface area costs you extra heat, even if the marginal loss decreases with growing tank volumes.

[0] http://www.fsec.ucf.edu/en/publications/pdf/FSEC-PF-464-15.p...

You can use warm water to power your heating in winter. So it might be less efficient in summer, but the amount of energy you’d save in winter would exceed the losses in summer.

In general, the bigger the tank, the better the 'skin to volume ratio'. Hence I'd expect less % per second of loss. The total wattage of loss would still be higher though.

Perhaps legionnaires' disease has something to do with it instead?