You're overthinking and confusing yourself. Locating energy off grid is far cheaper than connecting a source to a grid. It's a free voluntary global market and it is a competition, obviously. Like any competition, those who are uncompetitive either find a way to compete or accept they will lose.
> If China has the cheapest energy and 80% of the miners in the world pay to physically locate their rigs there, can't a single country take over the entire network at a whim?
Hypothetical and immaterial. If no one else in the whole world can compete with China's cost of energy production then we have much bigger problems to focus on than mere bitcoin mining, for China will simply leapfrog the rest of human civilization technologically and economically.
Also, see: - https://www.coindesk.com/policy/2021/06/22/go-west-bitcoin-u...
- https://www.coindesk.com/business/2020/05/19/the-last-word-o...
Irrelevant because whether costs are internalised or externalised is up to the humans in a jurisdiction to decide. If you choose to legislate yourself out of competitiveness in any field, that's your choice. Finally, everyone in a free market is incentivised to reduce cost basis and increase efficiency. So, nuclear.
You can't credibly say "I'm not sure what the difference is" and then say "except for the actual difference."
Throwing millions at Bitcoin mining will work if and only if you also have access to cheap energy. The only way to turn a profit is to have access to cheap energy. The key component isn't hardware but energy. (You can see this in how old mining rigs become profitable as price rises.)
It is in this way, the fact of required cheap energy, that Bitcoin enables decentralised mining. There is a strong incentive for any energy producer, and a race amongst energy producers globally, to source the cheapest energy because they can mine Bitcoin with it, no matter where on the planet, no matter how remote or off-grid the energy is as long as they can connect their miners to a satellite or fibre connection, hash blocks, and earn bitcoin.
Is this democratic? It doesn't sound like it. But if democracy is "rule by the people", and people are distributed all over the planet and energy resources are also distributed all over the planet, and these people are free to organise their sources of energy, then anyone is free to mine, whether from home[0] or industrially.
In proof-of-stake, there is no such natural/physical constraint to centralisation. Capital simply isn't distributed the way energy is. It seems also that there are incentives to acquire as much capital as possible to control the pos network. Is this certain? Hard to say but we will soon get to find out.
The number-go-up thesis for Ethereum's proof-of-stake seems to be something like: we can get something for nothing: the more that controllers of large amounts of capital stake for sweet rewards, the more eth is locked up, the more eth supply is constrained, the more price rises, the more profitable it is for everyone else to simply stake. In this endless spiral upwards, everyone will be forced to stake simply to earn increasingly valuable rewards.[1] Perhaps they've engineered a kind of democracy?
[0]: https://www.econoalchemist.com/post/home-mining-for-non-kyc-...
[1]: https://twitter.com/SquishChaos/status/1387074095007817730?s...