I've boiled this down further, I think -- a more concise explanation, for reference:
- Alice wants to Pay Bob 0.5 BTC
- Alice sends 0.2 BTC to Deposit Address A, followed later by 0.3 BTC to Deposit Address B
- Coin Z (0.5 BTC), somewhere else, is sent to Bob and is entirely unconnected to Alice's deposits
More,
and most importantly:
- Coin Z went through 200+ separate CoinJoins over a period of 6 months
- The Coin Alice Deposited at Address A, later on that day participates in a CoinJoin
- The Coin Alice Deposited at Address B, participates in a separate CoinJoin 2 days later
- Alice's Coins are CoinJoined 20 or even 200 times before they even make their way back out of the mixer
In this scenario, it is very obvious that coin Z is from a mixer, and analysis can be done accordingly. It is also obvious that Alice's two deposits are going into the mixer.
The delaying of starting CJ transactions does nothing because there is a pattern of going directly from the deposit address into CJ transactions, and it would be obvious that both deposit address A and deposit address B received coin that went into the mixer on the same day.
Most mixers have known addresses and clusters to blockchain analysts, but someone studying a mixer may not know about all of the addresses belonging to a mixing service.