I would consider understanding this to be a necessary condition for advocating for (or using) BitCoin.
Also, one of the interesting outgrowths of focusing on the reachability of the network is that a few features of the network. Assuming the network is accepting all transactions, miners must be working on different subsets of transactions routinely. This implies that there's quite a lot of computation getting thrown out, routinely, as different miners start working on different subsets of transactions.
It also implies that there is a miner-to-miner DOS method, where the majority of the miner network blackballs a miner - no longer accepts their integrations. This is serious, but much less serious than an arbitrary public key freeze, which can affect anyone (your tumblers aside, it's always possible).
Finally, I begin to understand why Satoshi started with money. I suspect at some level this is not about money, but he needed to incent people to get this ball rolling. What is it about? It's about coherent, persistent truth. Transactions are just one kind of event that happens in the world. The pattern is valid for any global data-structure that you want to have great survivability and coherence. You might use something like the blockchain (adding back a little jargon) to store, for example, the mind state of an AI. The proof of work, rather than a mechanistic search for arbitrary hashes, might be somehow related to the operation of the AI's "mind".
Hmmmm. So, in order for someone to spend money, they just need one transaction in the blockchain moving the money to someone else. In order to cut them off, you need to make sure that transaction never gets mined.
Since there are lots of miners, even if you control part of the network, someone in the rest of the network could mine the transaction. Then you're in the position of having to refuse that block and maintain a fork. That's probably tenable if you control like 95% of the mining power. I'm not convinced that's tenable if you control even 50% of the mining power. If your victim keeps trying to transfer their money, you'll fairly often find the other 50% of the network having a block that you refuse to accept, and (I think) you won't be able to get your fork to reliably win automatically. IF you keep refusing blocks, it'll involve human intervention on the other 50% of nodes to consider your history the "real" history, and people will notice that something strange is happening.
You could, of course, accept the transaction, track their coin, and consider all money from its recipient tainted. But there are enough large wallets, like large exchanges and even tumblers (essentially money-launderers) that obfuscate the relationship between inputs and outputs. You're going to have to start blacklisting a lot of money if you want that approach to work.
> So, the root of banking power is currently institutional and legal, and all bitcoin is doing is giving that control to people with the most compute power.
Yes, this is basically my biggest personal disbelief about Bitcoin: many governments could out-mine the entire Bitcoin network right now if they decided that it was important to national security. I'm not convinced this is a fundamentally unsolvable problem (there are some alternative models, Stellar's consensus protocol probably being the most interesting) so I'm not a cryptocurrency skeptic, but I am a Bitcoin / proof-of-work skeptic. There do seem to be a bunch of people in the Bitcoin community interested in alternatives to proof-of-work, which I think is healthy.
(And relatedly, if we don't need proof-of-work for security, either because something else works or nothing possibly works, let's stop building a world in which we have to burn energy for currency transfer.)
> On a related note, I'd like to understand on a practical level how people reach "the miners" ... how do miners learn of unintegrated transactions?
I don't understand this clearly and I'm currently the wrong person to ask. The best I can find is https://en.bitcoin.it/wiki/Transaction_broadcasting plus https://en.bitcoin.it/wiki/Network (there's some IRC-style way of learning about nodes, and I think at the network level, ~everyone is a node and considered capable of mining). I suppose the paper might know more; we could look.