Definitely. In a (directed) tree there are exactly 0 or 1 paths between two nodes. There's no such thing as a shortest path. In an undirected tree there's exactly 1 path between any two nodes---even worse.
You might be representing a graph with a tree however if your nodes are labeled and you want to talk about the shortest path between two nodes quotiented by those labels.
Trees are very useful. Graphs are occasionally useful. But you can't really say what is useful until you know it. One of the sadder truths of education/learning.