Cartels will take over first. Once the cartels control 100% of mining, then the government will take over the cartels in "retaliation" (with winks and handshakes behind the scenes).
That is the normal course of events in democracy.
I don't think people will care if the 51% is owned by an organization that calls itself "cartel" or "government," either one will be considered a threat, and likely either one coming close to getting 51% will cause concern and threat of price collapse.
Fact:
The cartel can hide how much hashrate it has, by using many IP addresses and sharing transactions until it has 50+% or more and is ready to move to the next stage.
All transactions get propagated through the entire network of bitcoin users, with miners eventually also hearing them. So if you suggest that a mining cartel can somehow keep transactions from being broadcast, and keep other competing miners from hearing about them and mining them too, you are mistaken.
You are incorrect. If Amazon offers a downloadable client (or even one that runs from their website), which sends the transactions to their server, they have no obligation to forward the transactions to other miners.
So, if you are using an Amazon wallet app, and I am using some other wallet app, and you try to send me coins, how will I know whether you sent them if you only send them to Amazon's servers? It would essentially cut everyone using Amazon clients off from the rest of the bitcoin network. Why would anyone want to use such an app? Bitcoin transactions primarily work because they are propagated P2P through the network from person to person. Miners just sit on the perifere catching these transactions as they pass by and adding them to blocks.
Fact:
You are conflating the publication of block solutions with the propagation of transactions before the fact.
You don't understand well the way Bitcoin works.
I mean, can miners screw with Bitcoin by implementing arbitrary rules, such as increasing the total number of bitcoins, or creating nonstandard transactions, and forcing everyone else to eat them.
Cartel can once it has destroyed all other miners and has 100% of the network hashrate.
Once they get beyond 51%, the bitcoins they are working so hard to mine and get control of will start rapidly losing value, as people abandon it and move to a more distributed system. Even getting close will be considered a threat. Just knowing this is likely to keep anyone from trying.
Fact:
If the cartel waits until they have 80 or 90% of the hashrate and transactions before attacking, then you will not get most of the commerce on your new fork. You lose.
The cartel's customers are not going to change which websites they send their transactions on. They will be happy with the service they are getting.
This is known as installed base networking effects, or inertia.
Cartels will own 100% of mining. No improvement at all for humanity. Worse we will be on a public ledger with no privacy nor anonymity. This is the 666 system.
How would miners know which address belongs to whom, if no IP's are tied to it, and their miners may only hear about a transaction after it has passed through multiple clients? And don't forget, if a 51%+ cartel implements nonstandard changes, their blocks will not be accepted by any of the clients, and won't even propagate. Their 51% will instantly become 0%, because, again, bitcoin rules are enforced first by the clients, and second by the miners.
None of that makes any sense.