Using an exchange that has your identity means your activity on the exchange is discoverable, either by the bureaucracy, or by hackers.

Once you transition your money to a untraceable currency like monero, your activity after that point becomes undiscoverable.

When you use an ATM on a street corner to pull cash out, the ATM, the ATM network, anybody on the street, can see you pulling the money out. What you do if the money after that is up to you, and is less tracenable.

Whatever your use case, you have to factor in the above points, using an exchange is traceable, once the funds leave the exchange it’s not traceable. The rest is up to you