The abundance of vehicle trajectory data offers a new opportunity to compute driving routes between origins and destinations. Current graph-based routing pipelines, while effective, involve substantial costs in constructing, maintaining, and updating road network graphs to reflect real-time conditions. In this study, we propose a new trajectory-based routing paradigm that bypasses current workflows by directly utilizing raw trajectory data to compute efficient routes. Our method, named TrajRoute, uniquely "follows" historical trajectories from a source to a destination, constructing paths that reflect actual driver behavior and implicit preferences. To supplement areas with sparse trajectory data, the road network is also incorporated into TrajRoute's index, and tunable parameters are introduced to control the balance between road segments and trajectories, ensuring a unified and adaptable routing approach. We experimentally verify our approach by comparing it to an existing online routing service. Our results demonstrate that as the number of trajectories covering the road network increases, TrajRoute produces increasingly accurate travel time and route length estimates while gradually eliminating the need to downgrade to the road network. This highlights the potential of simpler, data-driven pipelines for routing, offering lower-maintenance alternatives to conventional systems.