I'm not sure I understand the part about set theory. If anything, a valid use of DISTINCT is if you want the result to be (closer to) a set, as otherwise (to your point, depending on the data model) you may get a bag instead.

In fact, IIRC, using DISTINCT (usually bad for performance, btw) is an SQL advice by CJ Date in https://www.oreilly.com/library/view/sql-and-relational/9781...