Articulation Vertex, significance and real world usage?
First, yes, probably.  One example is when we wish to split the graph into its sets of biconnected components.

Second, I think you misunderstand the purpose of the exercise.  The goal is to teach you to think in terms of graph algorithms, not necessarily give you the solution for existing real world problems.

Most real world problems differ slightly from textbook exercises and examples.  But the goal is to give you a toolbox so you can handle similar problems.

It is also important that you understand what an articulation point (or a cut vertex) is, as well as the similar concept for edges (bridge), so that you get a better understanding of graphs and graph connectivity.  It is crucial to understand the concept of cut vertices and bridges before lifting the definitions to their more general versions on vertex- and edge-connectivity (separators and cuts).