There exist several fundamental problems with item statements system at Wikidata as well as with categorization system at wiki projects. Broadly speaking, Wikidata statements miss some functionalities of categories, categorization system misses some functionalities of statements, and both systems have some common limits and system problems which can be overcome in similar way.
Most of statements are designed as reciprocial (the define relation between two items) but they don't work really as reciprocial. Statements are not able to be chained to threads - that fact leads to the situation that many used statements are paralelly redundant, and the whole system of statements is chaotic, not transparent, unmaintainnable. Categorization system have both these problems splendidly resolved. The edit interface is heavily clumsy and disorganized.
Categorization system is very complex, transparent, intuitive and easily maintainnable, However, it don't enable to distinguish a type of relation, which impedes to extract (filter) purely hyponymic or purely meronymic threads from the structure, when needed. There are also problems with relations, which are not clearly hierarchic (People should be a subcategory of Anthropology, or Anthropology should be a subcategory of People?).
A problem of both these systems is that the connecting elements are not autonomous but are a part of one of the two connected items. In the categorization system, the connection is a part of the lower item page. At wikidata, the relation need to be additionally duplicated (rendered) to the reverse statement in the opposite item. If we will separate the connection elements to autonomous elements, we can reach higher universality of both systems, real functional symmetry of relations, and using suitable qualifiers, we can archive history of the relations and link it with the history pages of affected items. A qualifier can also limit the relation to a specific project, as well as share identic relation by more projects. Such a transformation would open doors to crystallize a meta-categorization structure which can be helpful support for construction, compatibity and mutual influencing of local categorization structures in particular projects.