After an answer is accepted, sometimes a much better answer comes along, maybe even showing the accepted answer wasn't such a good idea after all (example). When the new answer is published, the original posted gets notified immediately. However, he may not know at that time if the new answer is better and worth trying.
If over time the new answer accumulates many upvotes, far outpacing the first answer, it would be helpful if the original posted received a notification, highlighting the popularity of the new answer, and encouraging him to change the accepted answer if appropriate.
A side benefit: less experienced users would learn that they can change the accepted answer (I think many don't know that).