==> you see the error in your reasoning: it is not because Satoshi "attempted to create" something, that the something he created, will behave the way he intended it !  Taking the desired outcome of a design as a logical consequence of the functioning of the design is a known error which happens frequently in discussions about bitcoin.


I think you're slowly getting it.  The public proofs are not to "show that the miners behave well", but only are there to prove your transaction to someone else, in order to obtain value against it (an IOU on an exchange, drugs on a dark market, whatever you want to use your transaction for).  Because if you, as a user, owning a lot of bitcoins, are not happy with the single ledger out there, and find that that single ledger is not built according to how you think it should be built, then you have only one single option: leave your bitcoin holdings for what they are, and go farming or sailing and forget bitcoin.   
Indeed, the ONLY MEANS you have to obtain value against your bitcoin holdings, of which the sole proof resides in the sole chain that is being made out there, is for that single chain out there to record your transaction, with the hope that the recipient is going to be willing to consider it as valid.  If he doesn't, you've simply lost your coins on that chain.  If you don't consider that sole chain as valid, you're foregoing your "right to spend" of your coins, because it is the only place where you can spend them.

I know that Satoshi *intended* it otherwise, but that's how the system that he designed, is designed to behave.  This is because Satoshi saw the whole network as mining or at least, as the miners embedded in a P2P network.  But if the mining nodes are not very numerous, and have a backbone connection, then the P2P filtering doesn't affect them in their building of a chain.

So essentially, if "users" on one hand, and "miners" on the other hand, are united, and miners make only one chain, and users refuse that chain, then:

1) users forego all their rights to spend, as if they didn't hold any coins
2) miners are making coins nobody will buy

I think SOME users will give in first.  Because they are more numerous (millions against 20) ; because they have individually no cost in "leaving their camp" (while miners do, especially with the very slow difficulty adaptation of bitcoin).  Users remaining united against miner consensus is a "tragedy of the commons": the user that switches behaviour WINS (can buy cheap coins from miners and can transact!).  The miner is in a Nash equilibrium with other miners, and forking off is expensive for him (his chain may not survive).

Game-theoretically it seems quite obvious that "united users" against "miners in consensus" makes the miners win.

What is tricky, for miners, is to get into this different consensus.  There, most probably, they can only do so with cartel formation, because they are in a Nash equilibrium in the current protocol.  But we are talking about the hypothetical clash between the miner protocol and the user "verification". 


No, that's not what I'm saying.  I'm saying that a dynamical system behaves the way it is observed to behave, most probably according to the emergent properties of the dynamical laws of its constituents, and NOT according to some pre-conceived ideas from how it SHOULD behave because it was the DESIRE of the founder or something.   I'm not saying that there are no true laws of gravity.  I'm saying that the laws of gravity are whatever we observe gravity to do, and even if we would think that gravity SHOULD behave differently for moral reasons, that's not necessarily going to happen.

In other words, bitcoin has dynamical rules built into it, which are game-theoretical and cryptographic/techical.  These rules will determine how bitcoin will behave ; and not some or other white paper.  That said, in as much as the author of the white paper correctly estimated the emergent properties of his design, that design will work as designed ; and in as much as he made mistakes, his opinions don't matter, but the real behaviour does.  Real behaviour which must find its explanation in the behavioural rules of each of its entities, as confronted to the "rules of engagement" (cryptographic and game-theoretical).  Whatever results from these interactions as emergent property, is what we call bitcoin's behaviour, and hence, the "valid" way in which bitcoin acts.


This is not necessarily true.  After all, are you really going to say that if miners start mining 20 MB blocks tomorrow, that nobody is going to value a bitcoin any more ?  The value of bitcoin has only to do with the belief in the value of the buyer of the coin. 
Do you think that big owners of bitcoin are going to let their stash become worthless, because some or other protocol changed ?  Of course they will try to convince greater fools to buy their coins, exactly like they are doing right now.

That said, you are right that miners will be sensitive to the valuation of their block rewards (coin value times how many of them they can obtain, fees, and block rewards). 
In fact, if they would estimate that the price of a coin would divide by 10, but they would be able to obtain 20 times more of them, that would be a smart move on their part, doubling their income.

But it would be difficult for them to make that move, because they are individually locked into a Nash equilibrium with the current protocol.  Only cartel formation would let them do so.