You are saying it is trivial but still don't give an answer to a simple question: how are you going to decide which UTXOs are worthy to be a part of a CoinJoun transaction and which are not? This has nothing to do with privacy leaks or publicly available information. It is about censorship of bitcoin transactions and attacks on its fungibility. Everyone knows chain surveillance companies always try to make bitcoin less fungible, but they can't censor it, except through companies like zkSNACKS that voluntarily decide to help censor bitcoin.

You also said that the "coordinator can't collect anything" and that it "only knows of the UTXOs to take part in coinjoins - so does the public." Both these statements aren't true because the coordinator knows all the UTXOs willing to participate in a CoinJoin while ordinary users only know which UTXOs are theirs. Only after a CoinJoin transaction has taken place, can ordinary users learn which UTXOs were allowed for participation. Therefore, they can't censor transactions, they can't chain surveil blacklisted users, they can't know who was rejected and why.

A coordinator, on the other hand, knows everything and can collect information about all unsuccessful attempts of registering illegal UTXOs and particular points in time of these attempts. For example, after a certain period of inactivity hacker wants to cover the trace of stolen funds and registers "tainted" UTXOs in Wasabi CoinJoin. A coordinator immediately notices that, rejects those UTXOs, and informes law enforcement agencies that a hacker was active and wanted to mix his coins. Will this help to catch him? Maybe not. But the fact that a privacy-oriented wallet tried to invade the privacy of one of its users, albeit a criminal, will scare those who are honest.