There are exchanges that have the option of requesting the deletion of data after the order has been executed. And mostly, it is desirable that they be deleted as soon as possible.
Later, we are surprised when a service is seized, and it is announced that several terabytes of data were also found.
If someone wants this kind of data to be stored for a long time, then do not choose a no-kyc service or a service that is in some way privacy.
The recent case is of ShipMonk. Trezor was using it for shipments, and the last breach reported data of 13,689 people. Everyone praised Trezor and ShipMonk because there was an agreement between them to delete data after 90 days, but now things have changed completely. The same breach has now been reported, and more than 80k people have been affected by this breach, and the data that ShipMonk was never supposed to keep was stored anyway by violating the rules and is now in the hands of hackers.
It is not an exchange, but still, it is relatable. We can't trust any platform these days, that's for sure. Therefore, we have to cover our tracks if it's that important to you. As safar1980 above said, XMR can be a better choice for you.