|Don't ask to ask, just ask|
Ouch! You're right.
This need to be a one-stop-shop for all data structures gets back to your informative dialog with John M. Dlugosz. However in that thread I feel your claim to focus on objects seems a bit disingenuous: If you have no equivalence method to call, then your intersections are always null. To use your imagery, elements in different sets of employees that could be twins are never identified.
(Here I address a rebuttal that is not necessarily yours. I just like using second person in threads.)
You then could claim that you are only interested in identity, not equivalence, and that you get identity from stringification; so non-trivial intersections are again a possibility.
However, this claim would imply that stringification defines a bijection between objects and their hash keys.
Ergo, hash keys are all you need! ;-)
That being said, if you carry the values with you, then your gratification is more immediate, so despite my efforts and protests, we should just go ahead and scrap my attempts in the name of efficiency. This whole thread turns out to be a roundabout way of me agreeing to whatever it is that you and John M. Dlugosz hashed out (sic).