I don't think "computers have caches that are faster to access than main memory" is just an implementation detail though; if you're designing data structures for a specific kind of storage you should teach the properties of that storage first and the data structures after.
If you are designing data structures for a specific kind of storage, you have hopefully studied them beyond the first/second year algorithms and data structures class. Like most introductory classes, that class mostly teaches you concepts and ideas.
My job is largely about designing and implementing new data structures. Those four levels of abstraction are the ones I've personally found useful. None of them deals with implementation details, as they are all abstractions. Implementation details are an orthogonal concept that is relevant at every level.
