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".