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Energy Waste Fallacy
There is a theory that proof-of-work (PoW) wastes energy. This implies that the level of security provided is greater than necessary or the same level of security can be provided by another externalized proof at a lower energy cost. An internalized proof, specifically proof-of-stake (PoS), is a different security model which is not considered here.
Total hash power is a function of reward, which is a function of fees, which are determined by the confirmation market. If a person considers current hash power insufficient to secure trade at a given value against double spend then the depth requirement increases. Additionally, as shown in Utility Threshold Property, transactions with insufficient value for even single confirmation security are priced out of the chain.
These upper and lower security bounds depend on confirmation cost and are therefore independent of the proof technique. There is no necessary level of security, just a subjective confirmation depth and minimum utility.
Confirmation security increases with the cost of generating each block. The double spend of a transaction requires that its branch be superseded by another with a probabilistically greater cost. So the only way energy cost can be reduced is by expending the same average per-block cost with a lower energy component.
PoW incurs cost in several forms, including labor, hardware, services, land, etc. Any other externalized proof consumes these same resources, though potentially in different proportion. The question of energy cost reduction is therefore reduced to whether an energy component of the cost of a proof can be replaced by an other resource component with the same cost. However the cost of the substitute resource includes all of is production costs, which must resolve to energy. The theory is therefore invalid.
Additionally, securing any coin has a cost to merchants. As such the fact of its use by them implies that it is preferred over alternatives. This implies the alternatives are ultimately more costly. As all costs are fundamentally resolved in energy consumption, it follows that the money in use is the most energy efficient.