Sure, there are both interesting and practical uses of mathematics.

However, venn diagrams are not synonymous with set theory. Venn diagrams are a type of visualization, and once you're dealing with 11 overlapping sets... I don't really see the utility, since these are not human friendly and don't help viewers understand the relationship between sets and their intersections.

There are practical uses for much math but in very many cases it's only practical in extremely specialized fields/cases. Meaning, in most cases very impractical if speaking strictly in terms of practicalities. Yet, it's widely taught, widely misunderstood, and so widely hated. The idea has become humorous to me -- math, a natural pervasive wonder of our universe, hated by many. Very impressive feat.

On this topic this book is great: A Mathematician's Lament by Paul Lockhart. It opened my eyes to the concept of viewing much of math not in terms of something strictly practical, but rather in broader terms, ie. natural art and beauty with very practical applications mixed in here and there. Just as one person enjoys painting, another enjoys dabbling in mathematics taking pleasure from the elegance.

The essay that preceded the book is also food for thought. It's freely available online: http://www.maa.org/devlin/LockhartsLament.pdf

This isn't set theory.

(Venn diagrams can be interpreted in a set theoretic way, but this isn't particularly useful within set theory itself, and the symmetric and simple properties of the Venn diagram are unnecessary for this interpretation. We've had a construction for a simple Venn diagram of n curves since Venn's original paper -- it's the symmetry that's new.)