I think a great point could be made where all the data has to be retained. If I removed customer information and put them in as a guest, then I have no record of them any more. It would make it impossible to follow other eu laws.
For instance what happens if they want to return a product for a warranty? I would not have their data any more, just generalized order data. I could refuse their return saying I cannot be sure if you were the original purchaser, the warranty was not transferable
At the same time, if the government accused me of lying about where the shipments were going and said you did not really ship this many shipments out of this higher tax zone I would have no way to defend myself. I could not give them verifiable people that purchased the goods.