No you don't, which is why you're still talking about it the way you are.

> you have failed to mention any counterexample.

What we have now. Inflation debasing your money.

This is actually a game theory problem. There are three groups in bitcoin. The users, the holders, and the miners. To understand the way that relationship works, you have to understand what keeps everyone separated and honest. That requires an understanding of the incentives of bitcoin, and that requires understanding what proof-of-work (https://en.wikipedia.org/wiki/Proof-of-work_system) is.

Proof-of-work aligns consensus with the users, because it is the users that are paying the miners through transaction fees. Even holders require users, and more importantly, node owners. Therefore, it is users that are incentivizing the miners. Proof-of-stake (https://en.wikipedia.org/wiki/Proof-of-stake) aligns consensus with the holders, who are paying the miners. That is an incentive structure that reflects our current financial system. But bitcoin changes this through incentive structures and cryptography. In bitcoin, it is the incentive of the payers, not the paid, that imo is the wild invention of satoshi, and enacted through cryptography.

PoS fails because there is only one outcome given that incentive structure. Holders being miners, and then controlling the users. PoW overcomes this because the outcome is the constant tension between all three.

At the heart of the solution is what was previously thought to be the unsolvable byzantine generals problem. (https://en.wikipedia.org/wiki/Byzantine_fault_tolerance) It is a variation on the two generals problem. The problem is "if you are a number of generals surrounding a castle, how do you coordinate an attack date and ensure that the message to attack is correctly received, when you know that the message may be altered along the way?". There's game theory around what is possible, but that's the gist of it. In the problem, a bad actor can game the system so that everyone loses. I have reduced it to three. Given you know one is a traitor, how do you deliver the message to attack?

The way that this is managed is that miners order the transactions, and race to hash them to an algorithm (the work in proof-of-work), which is in bitcoin, SHA-256, until they get an answer that will be accepted by the nodes (proof). They are incentivized to become more and more efficient, and spend more resources as the price increases. The nodes provide the proof in proof-of-work. They say "this block is valid", and all nodes that follow consensus will come to the same agreement. For that work, the nodes award miners bitcoin. The nodes can prove which miner spent more work, but it sometimes takes a few blocks to get it right, which is why you have to wait for a few confirmations.

The only real thing that miners can threaten to do is stop users (the people paying them) from receiving blocks. Users and holders, after all, control their own cryptographic proofs to the tokens. But the current miners are only miners of SHA-256 pow algorithm blocks. In an adversarial condition, the miners will have just stopped coming to the party, so the users say 'fuck this' and change the pow. They get a new set of miners, mining a new algorithm, and the holders go 'holy shit, do I wanna spend my cash with a bunch of numpties that couldn't behave themselves?'. And they start spending their cash on the chain that the users say is the real one, and everyone just goes about their business again. Old miners get crushed. New miners think happy days. If the nodes change their software, that's the end of the story. Because the nodes define the consensus, they can. The remaining node owners get to decide whether they want to be owned by the miners, or whether they actually want to still remain users. The holders decide whether they are more likely to be able to realize their money with the miners that now control a drastically centralized subset of nodes, or to continue on in the system that led to them being holders in the first place.

Users can't attack the system, because then they would become holders, and users would no longer trust them for the reasons already stated, and they don't hold the cryptographic proofs of the holders. If the holders do that, they lose all of their users, so the only thing they game-theory-wise would do, would be to instate a pow. Why would anyone prefer a system in which the people with the money have all of the power? Otherwise known as the world financial system.

Whoever attacks loses, and there's no real way to cheat the system. That's the brilliant solution to the byzantine generals problem. It is a self-sustaining financial system that rewards everyone for participating in it, where incentives are perfectly aligned for its longevity, with an ever reducing supply of tokens that are effectively infinitely divisible, increasing their value per-capita. And no, there isn't any other system in the world that shares these properties. Without these properties, the byzantine generals problem can't be solved, and decentralization can't be achieved. It is a fiendishly clever system, akin to an anti-body to debt-fueled inflation.

Like I said, SN was/is/will be a genius.

> Eventually, you will run out of fools.

That is what is happening to the fixed-asset debt bubble. Bitcoin is its reckoning.