Air transport improves accessibility and can make travel more affordable, but it also increases environmental burdens and pressure on tourism destinations, dimensions that are still often examined separately. This study develops the Air Transport Sustainability Tension Score, a framework for individual routes that identifies where mobility benefits and sustainability burdens coexist across European air connections. The analysis covers 11,065 directed routes and integrates accessibility, relative affordability derived from expected fares, environmental burden, and destination tourism pressure. Accessibility and relative affordability form the benefit dimension, while environmental activity and tourism pressure form the burden dimension. Their harmonic aggregation limits compensation and assigns high scores when both dimensions remain elevated. Relative affordability was derived from expected fares generated for each route through five-fold cross-validation with Ridge regression, Random Forest, CatBoost, and XGBoost. Each prediction therefore came from a model that excluded the corresponding observation during training. Among the evaluated fixed model configurations, XGBoost performed best, achieving a mean absolute price error of EUR 28.58 and an R2 of 0.6871 on the logarithmic price scale. TreeSHAP was then used to interpret the model predictions. The environmental activity proxy correlated strongly with the strict CO2 score derived from fleet information on 3622 routes. Across the sensitivity analyses, the broad route ordering remained comparatively stable, although exact membership in the upper decile was more sensitive to methodological choices. The primary upper decile contained 1107 routes. Monte Carlo weight variation retained 580 routes and the complete specification multiverse retained 506, with 421 supported by both procedures. Two route archetypes revealed distinct empirical profiles involving strong connectivity and environmental activity or greater tourism pressure at destinations. The framework provides an interpretable basis for differentiated air transport and destination management without automatically classifying routes as sustainable or unsustainable.