Technically a Venn diagram's entire point is to visualize all possible set relations between N sets. Their "practical" use is explicitly visualizing this.
In popular terminology they are very often confused with Euler Diagrams [0] which represent meaningful relations in sets but not all possible. You shouldn't create Euler Diagrams this complex, but the raison d'etre of Venn diagrams is to visualize the complex nature of set relations.
There is always the complicated wires puzzle from "Keep Talking and Nobody Explodes". Where a 5 way Venn diagram encodes what action you need to take for a given state.
