Yeah that is kind of logical, there are some caveats. The miner has a lot of capital invested maybe > $300m to do that now. (You can be sure most pool miners would abandon a pool that did that.)
I am not so sure... If the change to the protocol means not having their revenue cut 50%, I bet that most miners, even those who are not in the cartel, would eagerly support it.
Merchants who "accept bitcoin" would not care and would not take sides, since they receive dollars and, at worst, may lose some customers if bitcoin collapses. Payment processors, exchanges, and the like would have to choose a side, but since siding against the cartel could mean losing their income for months, they will probably upgrade before the deadline; and that will force their clients to upgrade, either before the deadline or before accessing their services again. Note that, up to the deadline, users and miners who choose to upgrade will continue to interoperate with those who don't.
I seems that when people discuss a 51% attack they assume some entity that wants to either destroy bitcoin, or pull some quick scam (like double-spending) and run away. But cartels usually employ their power to maximize net revenue over the long run, and are careful not to kill their cash cow.
This is going to be disruptive to bitcoin confidence and price and that affects the value of bitcoins they are mining, or the equipment itself which is worthless if bitcoin fails or crashes badly as a result. Dangerous game to play with a $300m good behaviour bond.
At the current BTC price, the change I described would mean 600 k$/day for 2 years for the whole network, which is ~440 M$. If the cartel has >50% of the power, that means >220 M$ of extra revenue just for the cartel.
Depending of their costs, that could mean the difference between making 100 M$ profit (say) if they try and succeed, or having to turn off their equipment and lose all their capital, as a reward for their "good behavior", if they do nothing. At worst, if they try and fail, they will lose only a few weeks of revenue; and from then on they would get the same "reward" they would get if they did nothing.
Moreover, I don't believe that many people would want to leave bitcoin just because of that change. Not even the long-term holders should change their minds about bitcoin's future because of a change to a parameter that was clearly chosen quite arbitrarily. (People in countries with high inflation or bank deposit haircuts do not stop accepting their currency; they just try to spend it as fast as they can, or convert it to investments that are resistant to inflation.) The price may even go up, if the change is properly marketed as preserving the network's unique strength etc.
Secondly while they are DoSing bitcoin, they are not mining coins nor on their proposed alternative chain at any kind of usable speed as they have almost no hashpower left (if they have 55% and they're using 53% to DoS bitcoin that gives them 500min blocks if the new chain has the same difficulty. If the new chain has reset difficulty the honest miners might DoS it in retaliation (block transactions there). Now if the attacker had maybe 70% they could dominate both chains reliably.
The cartel would have to change the difficulty level and the difficulty adjustment algorithm to keep the new chain flowing at an acceptable rate during the transition period. The cartel can move its power back and forth between the two chains, according to what the non-cartel miners are doing, in order to always have 51% of cooperating hashpower on both chains. As noted above, most of the non-cartel miners would have strong incentive to cooperate with the cartel, and upgrade to the cartel's protocol, before the deadline; they would then put any rebel miners at an even bigger disadvantage.
This is beyond mining a new hard-fork protocol version (which honest users and full nodes would ignore) and more DoS warfare to kill the main chain to give users a choice of no transactions or to fold and use the new chain. I would imagine users would be annoyed enough about that so as to be a scenario where the bit red button might get pushed - destroying the $300m capital of the attacker (and the $245m of the rest of the miners who probably are going to sue the attacker, and its not easy to hide the delivery and location of $300m worth of mining equipment drawing perhaps a GW of power.)
I still do not understand what sort of "big red button" could do that. Changing the protocol to make the ASICS useless would force any remaining rebel miners to give in to the cartel, and would require that the rebel users upgrade to a different protocol (which is supposed to be a catastrophe) leaving them on a junk coin with a minuscule network, no service infrastructure, and a minority of the former users. But they would still have the option to upgrade to the cartel protocol and find all their coins waiting for them in the cartel chain, apart from any transactions that they made in the junk chain after the deadline.
Why wouldn't Bitstamp be already a sidechain, for example?
Well bitstamp isnt trying to algorithmically peg - they're saying trust our host security, cold wallet physical security, audit, governance / separation of duty etc. Ie you are trusting humans to manage an IOU. (Not saying bitstamp is a bad exchange).
I must be missing some essential detail. I understood that each sidechain would be just a black box from the viewpoint of the bitcoin protocol, and its designers/developers would be free to choose whether and how to peg its operations to the bitcoin chain -- without the bitcoin network having to know about it. Is there more to the 'sidechain' concept than that?
Could a sidechain be a BTC/USD exchange providing sub-second trades with cryptographic certificates? It would not be possible to peg every such trade to the blockchain, right?