This is where a study by the Feds (I think?) comes in. They found that they were generally able to link accounts as belonging to the same person, based on transaction patterns and flow of money between the multiple accounts the holder owns.

You can make it more difficult to link your accounts together by never transferring funds between your different accounts, but then how do you fund your accounts? It just gets more and more complicated.

I don't really think Bitcoin will bring an end to "Follow the money".

Not really. You can create new 'names', i.e. your wallet. But they start off empty. So how do you get the actual money (bitcoins) into the new wallet? You need to transfer the money from your old wallet/name to the new one. And that is publically logged. This means you can always follow the money.

The way to get around this is to generate many wallets and move things around a lot. However it's still money moving within a subset of bitcoin wallets, so potentially trackable still (Google is able to detect 'link farms', so the police might be able to detect 'mixing farms')

From what I understand, you need a 'cash remixer' that doesn't keep logs. The log deletion is what breaks the state chain.