Sure, this works if the mixing moves all coins through a single wallet. By using a set of different wallets where the control is shared but unknown outside of

Sure, this works if the mixing moves all coins through a single wallet. By using a set of different wallets where the control is shared but unknown outside of the mixer, you can end up with coins that are not traceable through wallets. A bit like you giving money to a third party, who calls up his friend, and then his friend gives the same amount of money to your friend. 'Your money' then ends up being used for something else (unrelated to you).