It's not strictly true in the sense that if the price were to fall over long enough periods of time, you would expect the hash rate to eventually fall, too.
But that's not plausible in the scenario where the world's financial system eventually runs on a proof of work cryptocurrency.
Since all miners compete over the same finite profits, each miner individually has an incentive to increase their hash power and therefore power consumption.
Even if the price was on average constant, the game theory would predict a competition over finding the cheapest way to burn the maximum amount of power.
Empirically, there were some transient drops in hash rate for both bitcoin and ethereum, on top of a constant massive run up.
But that's not plausible in the scenario where the world's financial system eventually runs on a proof of work cryptocurrency.
Since all miners compete over the same finite profits, each miner individually has an incentive to increase their hash power and therefore power consumption.
Even if the price was on average constant, the game theory would predict a competition over finding the cheapest way to burn the maximum amount of power.
Empirically, there were some transient drops in hash rate for both bitcoin and ethereum, on top of a constant massive run up.