Fatigue monitoring is central in association football due to its links with injury risk and tactical performance. However, objective fatigue-related indicators are commonly derived from subjective self-reported metrics, biomarkers derived from laboratory tests, or, more recently, intrusive sensors such as heart monitors or GPS tracking data. This paper studies whether monocular broadcast videos can provide spatio-temporal signals of sufficient quality to support fatigue-oriented analysis. Building on state-of-the-art Game State Reconstruction methods, we extract player trajectories in pitch coordinates and propose a novel kinematics processing algorithm to obtain temporally consistent speed and acceleration estimates from reconstructed tracks. We then construct acceleration--speed (A-S) profiles from these signals and analyze their behavior as fatigue-related performance indicators. We evaluate the full pipeline on the public SoccerNet-GSR benchmark, considering both 30-second clips and a complete 45-minute half to examine short-term reliability and longer-term temporal consistency. Our results indicate that monocular GSR can recover kinematic patterns that are compatible with A-S profiling while also revealing sensitivity to trajectory noise, calibration errors, and temporal discontinuities inherent to broadcast footage. These findings support monocular broadcast video as a low-cost basis for fatigue analysis and delineate the methodological challenges for future research.