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Just gave some more thought to this idea. I'm not sure if it's what you call timing analysis but a potential flaw is that split outputs may increase the probability of merge inputs when the payee use the received utxos. Even if we imagine that all txs (payment or pure mixing) are coinjoin txs...

Very interesting thoughts. Wrt using coinjoin for payments, I mean that by doing this, you automatically avoid the case of a user merging change from coinjoin tx with change from tx done after the coinjoin tx (alice in first example of OP). This point seems important to me because the main...

+1 for payment as output of coinjoin transaction. Imho, this is how coinjoin should be used.

Very interesting post. Just a point about the vulnerability through change linking. This scenario is a possible interpretation but not the only one. Imagine that instead of Alice sending 0.7 and receiving 0.3 for change, we have Bob sending 0.3 to Alice and Alice merging this 0.3 with her...