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

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.