> The Feds know that Dirty Money has gone to that wallet's address

They don’t. A wallet can have infinitely many addresses with nothing linking them together externally - only the holder of the wallet knows they’re related.

Think of a Bitcoin wallet as macOS’ Keychain or a LastPass account - and a Bitcoin address as the login credentials of each site you visit: provided you use a distinct login for each site, each site owner has no idea what other sites are in your LastPass/Keychain store.

Similarly: provided you use a new address for each bitcoin transaction then people you transact with have no knowledge of other transactions you’ve had.

People do often reuse addresses - however. Creating new addresses is free and instant - but consolidating your funds becomes a pain, especially if you have a lot of low-value transactions where the amount associated with each address would be eaten-up by the bitcoin network’s transaction fees.

And dumb criminals reuse addresses too - sometimes you see those “I have your password, send me bitcoin” emails using leaked passwords - and they all use the same (or a small number of addresses) - if this scam was run better they’d generate a new ransom address for each mail recipient. And I think that’s how they busted the operator and customers of the website in question: because they used a single address to receive funds at.

Ohhh, that makes much more sense. Thank you!

>> However many wallets Evil Criminal Mastermind makes, they're still going to be traceable by the Feds, right?

Yes, if:

>>ECM makes a new wallet, transfers BTC to it.

But if ECM initiates a new wallet with cash or other methods and doesn't tie their identity to it, then no.

You could trade your Bitcoin for Ethereum with A and then trade Ethereum with Bitcoin with B and you get back Bitcoin that can't be digitally tied back to your original source.

And where are you going to trade your Bitcoin for Ethereum and vice versa?

It may not be traceable directly through the blockchain(s), but the exchange destination will be, and they're almost certainly going to be complying with local laws which means they'll respond to a subpoena for data and give law enforcement whatever info they have on you, and most exchanges require KYC verification to handle any significant amount of funds.

Or Monero/other privacy coins to increase the gap.