on-chain tumbling can be effective at obfuscating the source of funds and making outputs fungible again.
There may come a time where mixed coins will be regarded with suspicion precisely because their fungibility has been restored.
Already happening albeit forced on them by their regulator -
https://cointelegraph.com/news/binance-returns-frozen-btc-after-user-promises-not-to-use-coinjoinAnd I have no doubt that many a privacy coin will be given the boot from exchanges as condition of staying open.