Your thoughts on abstraction here are exactly on the mark.
For the cluster-intersection thing, I think the biggest barrier is that “biggest cluster intersection” implicitly assumes some space in which the cluster intersection size is measured—some features, or some distance metric, or something along those lines. A more complex model will likely be using a different feature space, a different implicit metric, etc.
Your thoughts on abstraction here are exactly on the mark.
For the cluster-intersection thing, I think the biggest barrier is that “biggest cluster intersection” implicitly assumes some space in which the cluster intersection size is measured—some features, or some distance metric, or something along those lines. A more complex model will likely be using a different feature space, a different implicit metric, etc.