[SNIP]
IMHO architects who habitually visually embed elements are very lazy and inconsistent modellers.
I believe, what you meant to say was: architects who habitually ONLY visually embed elements are very lazy and inconsistent modellers.
Visual embedding is an exposition mechanism NOT a definition mechanism!
The problem with the metaphor (for the resulting diagrams) is that there is NO indication as to which of the relationships are being used. Of course, you mustn't mix them.
In our framework, we have instantiated the concept of the Generalization Set (Specialization Set) to allow multiple Set types. We see NO reason why the metaphor should not be extended to ALL relationship types, SO LONG as the type is clearly communicated.
It is the rendering of the instantiation of the set with the items visually embedded within it that indicates the nature of the set (Specialization, Aggregation, Composition, Association etc.).
The instantiated set element also renders the total set membership, whether it is disjoint and/or covering. Therefore you can tell if what you are seeing in front of you is the "full picture".
The set element is interposed between the encompassing element and the set members - both within the repository and on the diagram. You're not allowed to have a visually embedded element without having specified the relationship.
Paolo