Assume a reasonable computation model (thinking about pointer machine or RAM model), is there a problem where there is a clear separation between amortized and worst case complexity? Say, if amortization is not allowed and only worst case for each operation is considered, the time complexity will be (provably) higher. Notice that this is different from random self-reducibility.
Heapify is one example: https://www.geeksforgeeks.org/time-complexity-of-building-a-heap/
Another simpler example (Min / Max queue): https://www.geeksforgeeks.org/design-a-queue-data-structure-to-get-minimum-or-maximum-in-o1-time/ . This is also discussed here (see Szymon's answer): https://stackoverflow.com/questions/12054415/get-min-max-in-o1-time-from-a-queue
And there are many more...