Recent transportation research highlights the potential of autonomous vehicles (AV) to improve traffic flow mobility as they are able to maintain smaller car-following distances. However, as a unique class of ground robots, AVs are susceptible to robotic errors, particularly in their perception and control modules with imperfect sensors and actuators, leading to uncertainties in their movements and an increased risk of collisions. Consequently, conservative operational strategies, such as larger headway and slower speeds, are implemented to prioritize safety over mobility in real-world operations. To reconcile the inconsistency, this paper presents an analytical model framework that delineates the endogenous reciprocity between traffic safety and mobility that arises from AVs' robotic uncertainties. Using both realistic car-following data and a stochastic intelligent driving model (IDM), the stochastic car-following distance is derived as a key parameter, enabling analysis of single-lane capacity and collision probability. A semi-Markov process is then employed to model the dynamics of the lane capacity, and the resulting collision-inclusive capacity, representing expected lane capacity under stationary conditions, serves as the primary performance metric for fully autonomous traffic. The analytical results are further utilized to investigate the impacts of critical parameters in AV and roadway designs on traffic performance, as well as the properties of optimal speed and headway under mobility-targeted or safety-dominated management objectives. Extensions to scenarios involving multiple non-independent collisions or multi-lane traffic scenarios are also discussed, which demonstrates the robustness of the theoretical results and their practical applications.