With decent mixers, you can't link the coins because the link is broken. That's what traditional mixing does.
With Coin Join and similar methods, everyone in that transaction is linked, so you get lost looking at it. You can no longer trace one input to another output because suddenly 100 inputs goes to 100 (or more) outputs all in the same transaction. Boom, lost in the crowd.
And, if you just played on some dice sites, suddenly your inputs gets mixed with a whole bunch of others.
With mixers you have to trust a third party, they they (1) dont run with you bitcoins, (2) dont log everything which transactions are which, (3) you dont get dirtier coins than your own, (4) they are not run or infiltrated by feds.