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.

0. https://en.wikipedia.org/wiki/Euler_diagram

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.

https://bombmanual.com/web/index.html#ComplicatedWires

However you could make a good argument that having a complicated and confusing diagram is the point of that puzzle.

Agree, I think the linked Upset diagram is better.

Thanks, I was just about to do that!