If the price of bitcoin rose to $1 million, but the price to mine one and associated transaction fees stayed at, say, just $20k in electricity costs, don't you think lots of other miners would beef up their rigs to mine bitcoin now? After all, that's like $980k in free money!

Of course, they would beef up their rigs (spending commensurately more in electricity), and the required hash difficulty would go up to keep the mining speed at a block per 10 minutes.

Another way to think of it, is why do you think the electricity requirements of Bitcoin are now the output of Argentina? Years ago they were a teeny fraction of that. As Bitcoin became more valuable, the competition for mining increased, so the hash difficulty adjusted to ensure the new block rate matched the higher wattage miners were willing to put in to increase their hash rates.

That's a big assumption. Same assumption made in the study which provides the 0.5% world energy consumption figure that everyone is citing. No actual evidence that it is true is provided. The same study shows minimum consumption estimates which are much more reasonable.

I'm not assuming anything.

There is a guaranteed deep correlation between BTC price and amount of electricity needed to run the BTC network. That is the way proof of work is designed to function. I.e the whole way it protects against a 51% attack. There is simply no getting around this.

There is a relationship between mining difficulty and energy consumption. What I don't see is the correlation between price and mining difficulty. By this logic, mining activity should be way down right now.

I've read this explanation that i find explicit:

""" If 1 coin costs $50,000, and you already own the rig, it's worth spending $49,999 on electricity to mine the next coin and you will make a profit. If you're rig can't do that, you're better off just turning it off. """

Note that this is how it worked for bitcoin startup five years ago once the first specialized bitcoin rigs came into being. When the price of electricity where they operated became too high, some startup shut out or just changed their operations to create value around BTC(email/photograph ID/validation on the blockchain or other stuff like that)

I assume because the higher the price the greater the incentive for one entity to take over 51% of the network and start stealing transactions.