I think the next iteration is (or should be) a Dash button with an e-ink screen built in that can order any item and the screen changes to display the brand and name of the item it's setup to order.
Trying to add a changing ad screen to this would kill the battery life because of the check-ins to fetch the next ad. I also don't see that generating many sales because the customer would still need to change their set order, I think few people would accept Amazon outright changing what the button ordered based on the current ad.
As someone else mentioned though, think of it as "Dash, the physical button" + "Dash, the API". The API is probably the long term goal, the physical button is just a (temporary) drop-dead simple API client that people can use today. Amazon is likely betting on smart-fridges/-pantries/-homes catching up in the future
Edit: in the near-future, I imagine Amazon adding a touchscreen (so it's not product specific) without adding much to BoM. They can also charge manufactures for on-device screen-time (who doesn't like ads that convert to an immediate sale?)