Why unless? Say you have 1 ETH in Wallet A, if you transfer it to your on/offramp (the exchange) and then do Wallet B, the only link between Wallet A and B is only known by the exchange, so you'll remain private (publicly, again assuming you don't want to hide from the exchange).
You can't trust the exchange to not inadvertently leak the information. A substantial leak could include personally identifying information along with account balances and or deposit and withdrawal totals.
Somewhere along to lines, if you want USD, you need to trust someone, it's inescapable. So once you know this, you can act accordingly.
But still, the original argument was that you have to worry about chain analysis because everything is public, but obviously that isn't true, no matter if an exchange may or maybe not inadvertently leak something.
