Yes, the resulting tensor is incredibly sparse, but still too large to ever be practical for use as anything but the theoretical upper limit on the complexity of a model.

The issue is that while you can remove pretty much all possible interactions for a specific case you have no idea where an interaction could pop up unexpectedly with a huge impact ahead of time.

For the medieval theme the leader of the village may be a cousin of the king which is a very distant but very strong interaction.