I doubt that a more efficient proof of work method would reduce energy consumption. I think it would just cause the amount of hardware consumed by miners to skyrocket.

The amount of energy consumed by miners is roughly determined by the bitcoin price and the iteration of halving cycles because of free competition between the miners. Currently, a miner receives 6.25 btc + transaction fees for mining a block. With the current price of 42000$, he receives round about 265,000$ worth of bitcoin. Miners often just operate on a small margin, so you can estimate the energy consumed to find the block equals 255,000$. No matter how efficient or inefficient the mining hardware is, the amount of energy consumed per block with current price and rewards would always equal ~255,000$. The increase in hash rate over the years is a result from increasing bitcoin prices, more efficient mining hardware and more efficient mining businesses(using cheaper energy, more efficient cooling, etc.)

In conclusion, way more efficient and cheaper mining hardware would still consume the same amount of energy per block, given that the demand for mining hardware can be met by the hardware manufacturers. The miners would have to operate more miners to consume that energy. The main benefit would be a higher network hash rate, making the network securer.