Quantum communication research has in recent years shifted to include multipartite networks for which questions of quantum network routing naturally emerge. To understand the potential for multipartite routing, we focus on the most promising architectures for future quantum networks-those connecting nodes close to each other. Nearest-neighbor networks, such as rings, lines, and grids, have been studied under different communication scenarios to facilitate the sharing of quantum resources especially in the presence of bottlenecks. We analyze the potential of nearest-neighbor entangling gate quantum networks and identify some serious limitations by demonstrating that rings and lines cannot overcome common bottleneck communication problems.