I don't see how that would work unless you already had a priori identifying information for the person who performed the transaction.
If I deposit 500 BTC every Friday, and immediately transfer it into the mixing account, then order a pizza for 10 BTC on a Tuesday, paid for from via mixing account, how would you confirm that I was the one who ordered the pizza? All you can determine for certain is that (a) I am a subscriber to the mixing account, and (b) someone who subscribes to the mixing account ordered a pizza. If there are a million subscribers to the mixing account, without access to their internal records, there's no way to conclusively associate outgoing payments with specific subscribers.
If I deposit 500 BTC every Friday, and immediately transfer it into the mixing account, then order a pizza for 10 BTC on a Tuesday, paid for from via mixing account, how would you confirm that I was the one who ordered the pizza? All you can determine for certain is that (a) I am a subscriber to the mixing account, and (b) someone who subscribes to the mixing account ordered a pizza. If there are a million subscribers to the mixing account, without access to their internal records, there's no way to conclusively associate outgoing payments with specific subscribers.