That's exactly the issue.

Exchangeability and identifiability go hand in hand.

Take how exchanges, especially those that comply with KYC and AML measures will flag what may be considered "suspicious" Bitcoin addresses, when in reality they are simply addresses that use privacy features like CoinJoin.

Yes, it is the right of private businesses to refuse service, but at the same time, the fact that they can even detect addresses as suspicious and result in people not wanting to do business with said addresses should be proof alone of how critical the impact of identifiability has on exchangeability.

This is the advantage Monero has because its blockchain is not public, meaning tainted XMR is not as big of a problem as tainted BTC.