In network optimization problems, from traffic engineering to network monitoring, the routing model is typically considered as something given and frozen. This paper is motivated by the fundamental question how the ability to change and optimize the routing model itself influences the efficiency at which communication networks can be operated. To this end, we identify two main dimensions of a routing model: consistency (of a single route) and coherence (of sets of routes). We present analytical results on the impact of the routing model on the achievable route diversity as well as on the runtime of solving optimization problems underlying different case studies. We also uncover that it can sometimes be beneficial to artificially restrict the routing model, to significantly reduce the computational complexity without negatively affecting the route diversity much.