> Proof-of-work requires, by design, that the electricity value expended on mining is proportional to the total market cap of Bitcoin.
Proof of work in Bitcoin requires computation of a thing called a Nonce. If a miner gets the right Nonce while hashing, they get that block's reward. The electricity value expended on mining that block is proportional to the total amount of hashes being performed by miners in the network at the time. There is no "design" for requiring the cost of this power be equal to anything directly related to the market capitalization of Bitcoin, which really means how much Bitcoin is worth compared to other markets, such as USD. Are they linked to each other through human action and decision processes? Certainly. Is it coded in the chain? No.
> It's really just simple arbitrage: if the value of Bitcoin goes up, but the electricity cost doesn't, then you have essentially 2 different prices for 1 good, which should attract more miners to spend more money on electricity.
If the electricity cost doesn't go up, then the number of Nonce being computed will only go up if more miners join the effort. If they don't, the network is still operational, and produces the same amount of new coin every so often. What is NOT obvious here is that the technology for increasing the mining rates is always increasing, so the clowns will continue to pay to upgrade their hardware over time to save on electrical costs and engage in competition with the technology. The exchange rate for Bitcoin may be related to the technological "power" that is required to keep the network running and producing new coins, but less directly so related to the amount of power burned.
> Furthermore, it's, again by design, a competitive system
By design, Humans compete. The Bitcoin blockchain could be mined and run by two clowns in a tent if nobody else cared. It's not coded to be competitive, it's coded to be cooperative. This means the the amount of power spent on mining and running the network is a cooperative function. The amount of money spent on developing and producing faster hardware is a competitive function. The two together produce something that is chaotic and interesting.
Bitcoin does have a downside, and that is that it is a viral thing that cannot be taken down by any one person or organization. It would take 51% of those running the network to cause it to fork into two. It would take an impossibility to halt it. Maybe this scares some people and maybe it makes some people excited about the possibilities. Either way, we're going to need Fusion to run it in the future.