Can someone enlighten me?
I must be missing something since most people's solution involves more complication than I thought required.
Why couldn't a person just create a few one-time-use wallets, use tor and transfer the coin through those wallets to a final destination address, and then delete the intermediary wallets. Those addresses would never appear again in the blockchain, so how could someone prove they belong to you?
It's a question of how you got the coins in the first place, for one. If you bought them on an exchange and your adversary is someone who can find out which address you withdrew them to, you need to mix coins from other sources in to hide that. If your chain of transactions starts at address A and ends at Z, and A can be linked to you, it doesn't matter how many hops you go through to get to Z if there are no other original inputs than A in the chain of transactions. A mixer would alleviate this concern, but they may keep logs. You'd need to use several different services for added security. The odds of all of them being corrupt are lower than the odds of one of them being corrupt.
I don't think that's the kind of scenario most people worry about, though. IMO the more pressing question is: Do you want everyone you pay to be able to tell how much BTC you hold? I think it's tremendously unsafe not to employ some method of concealing your full holdings. Mark my words, one day someone will get tortured and killed for BTC because they paid the wrong person and they saw their customer is worth millions in this instantly transferrable currency.
For that purpose, simply moving funds through an exchange should suffice. I'd recommend at least separating spending funds from other holdings and taking care to keep the two segregated.