Consider the following sequence of events:
An owner of a small restaurant in Cincinnati, who spends a fair share of time doing paperwork and "compliance" tasks for her twelve employees also happens to be a crypto-savvyness 1%-er. She knows all that needs to be known about pushing crypto around the internet. In fact, for the purposes of this story, we will assume that Alice (the owner of this restaurant) makes no mistakes when doing her crypto thing. No such person exists, of course. And we can later complicate the story by saying "Well, what if she messed up riiight …here?" We can do that, but right now, for simplification purposes, we will assume no human mistakes from Alice. This is an "allegory"! Did I say?
Alice desperately needs another cook. For each of her existing employees, she pays some overhead (estimates vary) in the form of numerous taxes and time spent dealing with compliance and demands from multiple layers of government.
One day Bob walks through the door for some chicken. Bob is wearing a Bitcoin themed hat and an Ethereum themed tee-shirt. Seeing Bob, Alice, dramatically removing her green accountant's shade, has an epiphany.
"Hello, sir", says Alice. You are a crypto fan I see. "Yes!", says Bob, and what's more, I have the super-human ability to execute crypto transactions without making any human mistakes.
"MEE TOO!", says Alice.
So we make the "perfect actor" assumption for Bob too. Again, we can complicate things later, but Alice and Bob are both assumed to do the crypto thing correctly. When we say "Alice" did such-n-such in an untraceable way using Tor and three VPNs, we will simply assume that "untraceable" is what it is. Crypto code has mistakes. People make mistakes, but one simplifying assumption here is that the cryptographic magic that is used to keep something anonymous or untraceable is "perfect", just to short circuit a certain category of objections. They certainly may not be, but even in our real world, they are damned close already. Again, it's an assumption see?
"Bob, would you like a to be a cook?", asks Alice. Bob, for some reason glossing over the question of why Alice would know his name says, "Yes! Here, you mean? Yes! I mean, I don't know how to cook."
"That's fine. Let us have a private conversation in my perfectly-private office, Bob.", says Alice.
Bob, having seen this movie, enthusiastically follows Alice into her office at the back of the restaurant.
"Bob, do you know how to use crypto perfectly?"
"Yes, Alice. And you?"
"Yes, me also."
Alice: "Let me describe a compensation scheme I have in mind for you, Bob, and you tell me what you think."
"Ok."
Alice Describes:
"Bob, I will pay you a salary of $3,235 per month for you to work here 40hrs/week. Shop around, I think that's hard beat for the role. Note that this is less than the effective amount I pay my other employees in taxes and sheer-fucking-pain-in-the-ass."
"You mean 'opportunity cost'.", suggested Bob.
"Yes. Thank you.
So, first off, I want us to agree that this arrangement is an absolute secret. In fact, this room has been carefully sound-proofed and electronically scanned for "bugs", of which none were found. We are also in a hollow granite cube floating on a pool of mercury, which is in turn surrounded by a broad-band fractal copper mesh Faraday cage."
"Oh, neat!"
"It's all quite safe. We can assume that our conversation is absolutely private. You hear me, I hear you, no one hears us. No one."
Bob waited for Alice to wink at him.
"To simplify things for me, let us first convert your salary into Ether. According to my calculations, at the current rate, I will owe you one Ether per month. To further simplify things, our agreement will be fixed at 1 Ether per month. If that should for some reason become an unappealing arrangement for you because of market circumstances, you will need to renegotiate or quit. It's 1 Ether for now, and that's what we're sticking with."
"Sounds great to me!", says Bob.
"I'm sure you know how offline wallets are done. I suggest that you use an offline wallet. Please come back tomorrow with a piece of old trusted hardware that pre-dates the crypto-era that you can use to make a hierarchically deterministic offline wallet. Like a shitty old Dell from 2007?"
"Oh, sure! I got one of those! But the battery only lasts about 20 minutes."
"That's all we need.", said Alice.
The next day Alice and Bob are back in Alice's perfectly-private office.
"Ok, Alice! I've got my perfectly secure, air-gapped, laptop here, with 90% …no, 18% battery left, and I'm ready to press 'enter' to create my wallet.", Bob says with too much enthusiasm.
"Ok. Please proceed at your convenience". This time Alice did wink.
Bob creates an offline wallet, writes down the seed phrase on velum using indelible ink, folds it up and puts it in his pocket.
He then inexplicably stands up and smashes his laptop on Alice's desk repeatedly. After a few minutes of this, with skittles of plastic, glass, computer chips, and rare elements all over the office, and hissing fragments of battery still searing their way into the linoleum floor, Bob finally sits down and smiles at Alice.
"Dramatic.", Alice says.
Importantly, bob did not make a mistake writing down the seed phrase, will not be mugged on the way home or in any other way lose his seed phrase or have it compromised by another party, ever. Bob now has a guaranteed-anonymous, private wallet whose key is perfectly protected.
This is a lot of work, and more practical, less dramatic measures will get you close enough to perfect. You will not need mercury nor to smash your laptop.
The point is, it is humanly possible and even reasonably easy to create such a wallet. It is in theory completely secret and private. Bob, having created this wallet, now has a corresponding Ethereum address. We will call it bob.eth. Anyone can do this. It is not magic, it is not a question of whether the NSA has tried hard enough to find Bob's wallet. With the assumption that Bob was genuinely not being spied on while creating the wallet, and that the paper (velum) wallet is not compromised, Bob now has a perfectly secure, and perfectly private wallet. It is infinitesimally improbable for Bob's wallet to be compromised (which necessarily just means guessing it).
Also, Bob need not do this in Alice's special office. He need not do anything nearly this crazy. He could simply get a hardware wallet and a USB battery pack and walk off into the woods to set up the hardware wallet. There are many ways to achieve this. Why would Bob do this in Alice's presence after all?
Alice now has an address she can use to pay Bob. It is just a random number! It has no meaning to anyone other than Alice and Bob.
Let's assume that Alice also has such a wallet. Bob doesn't (yet) know anything about this wallet. Alice created it years ago. She traded her terrarium for 100 Ether in Jan 2016, and …that's about it; no transactions since then. That 100 Ether was all earned by PoW mining, all anonymously, except possibly some IP addresses if you really struggled to figure it out. I mean really struggled. And what would you do with this information? You know (maybe) who mined Ether that was for some reason then sent to Alice's wallet. That's not too useful if you're trying to sleuth out even one such "suspicious" tax-ower, let alone thousands...
It is from this wallet that Alice will pay Bob.
And so it goes.
Bob works happily for 1 Ether per month and now owns several yacht and Caribbean islands, not that anyone but his closest friends are aware of this. But he also likes Cincinnati and meeting new people.
Does Bob owe some taxes? He has no clue. "Isn't it as simple as presenting me with a bill?", Bob wonders. "Like some kind of numerical representation of this taxation I keep being told I owe?"
Every now and then, Bob needs to log on to The COINGroup corporate website and exchange Ether from that same wallet for dollars. Once he was visited by the IRS and, since they see this address and have watched its balance grow over time with great suspicion, and know it's being converted into USD, have a question or two for Bob.
Two sunglassioed men wearing gentleman's attire and guns stood at his door. "Hello, Bob. I'm Agent Smith and this is my associate Corporal Paine. We are from the Internal Revenue Service of America. We have serious questions about 'bob.eth', which you've been pulling money from and turning into our dollars. You wanna tell us what's going on, Bob?"
Bob, having been watching TV and eating some sort of pie politely raises his dish to the two agents, "Squat Cobbler?"