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1 volt per sq cm, easily enough to run a traditional watch, but maybe not a smart watch.

You misunderstand. The problem isn't that 1V is too low, it's that volts aren't a unit of energy (nor of power). It's like talking about how many meters someone weight or how many liters tall they are.

Yeah, and the point is that in theory 1V of voltage can be enough to power a city (if some voltage multiplier circuit is used).

(Consider a thought experiment: short-circuit that 1V electricity source: the amperage will be very high for a short amount of time, but then voltage will drop quickly.)

The issue is that how much power that electricity source can produce, and that amount is not linked to voltage.

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