This is why I always enjoyed getting larger sets, especially technic sets, as they always had rare pieces that were extremely useful for a specific function. For example, the shifter gate piece in the original supercar set:
http://www.peeron.com/inv/parts/6543
I don't know. I think a good selection of different pieces vastly expands your options. Some of the coolest models are the ones that use weird pieces in clever ways--my favorite example was an Audi R8 that used white rope pieces (very specialized) for the front LED lights.
Taj Mahal doesn't seem like a strong counter-example, in that although it seems to have many non-standard lego pieces, it still has a high pieces per type value (or as the author described it, few types per piece).
There is some real data, but it does look like a case of research confirming common sense. Anyway, it make sense once you see it, but I probably wouldn't have thought of it myself. I enjoyed it.
I think the key point is not that the number of piece type increases with number of overall pieces, but rather the nature of the relationship (sub-linear in log-log space) meaning that while number of distinct component types increases with number of components, it does less so the more components there are. In other words there is a sort of economy of scale. C.f. similar results in biological and municipal networks due to Geoff West et al (sorry for lack of citation; typing this on my phone). I get the sense this work is related to West's.
