Another plausible explanation is that omitting the items you bought means that you have to log back into Amazon and look at your purchase history to see what you ordered. That gives amazon several more touch points to get you to buy more things, including the "buy it again" button that they put on the page for particular items. It also makes it more difficult for you to search for the name of something you bought in the past to order it from a different retailer.
Seems incompatible. Making you log-in to advertise is a far less effective option than the ability to advertise products to you while you voluntarily use another service, i.e. your email. They could easily do the same adverts and quick order links from your email, but targeted adverts in your inbox is useful information to Google, maybe even better than purchase history since the recommendation work is already completed.
