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.
This is a perfect example of the limitations of old school social graphs. The number of people you talk to is just the first order effect. What about all the people that people in your company talked to? That has a non zero economic impact on you. Similarly for any other company that your company talks to, and so on and so on.
It scales super exponentially since each person is a member of an arbitrary number of groups and their actions have some non zero impact on each other member of the groups they are a member of, and each individual in each group with a member of which they have interacted with.
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.