In the video, 2 utxos were combined into 4 utxos. If I send all 4 together, won't that reveal common ownership and the coinjoin was for nothing? Or does it still make sense because there were so many different inputs to the coinjoin that it's still difficult to determine where they came from even if sent together afterwards? Trying to understand that
Coinjoins are automatic in Wasabi any time you receive a transaction or create change as long as your balance is high enough and fees are low enough. Waiting until you have multiple UTXOs to consolidate instead of coinjoining them one by one saves on fees, this tutorial shows two inputs being consolidated in one coinjoin transaction: https://www.youtube.com/watch?v=UbOAbXjzBJg
Discussion
Sending all 4 UTXOs together is the least private way to spend them since that would give a clue indicating the total amount you registered for that round, but it would not be fully effective since there are many input combinations that add up to that amount. Spending the private UTXOs individually or remixing them before sending your entire balance is the best way to handle them.
OK. Thank you. That's the way I understand it. But then consolidating 2 UTXOs in a coinjoin and getting 4 back isn't really consolidation, is it? The point of consolidation is to have fewer UTXOs after than before, because I want to save on fees when fees are high. No?