Respiratory X-ray imaging enhanced by phase contrast has shown improved airway visualization in animal models. Limitations in current X-ray technology have nevertheless hindered clinical translation, leaving the potential clinical impact an open question. Here, we explore phase-contrast chest radiography in a realistic in silico framework. Specifically, we use preprocessed virtual patients to generate in silico chest radiographs by Fresnel-diffraction simulations of X-ray wave propagation. Following a reader study conducted with clinical radiologists, we predict that phase-contrast edge enhancement will have a negligible impact on improving solitary pulmonary nodule detection (6 to 20 mm). However, edge enhancement of bronchial walls visualizes small airways (< 2 mm), which are invisible in conventional radiography. Our results show that phase-contrast chest radiography could play a future role in observing small-airway obstruction (e.g., relevant for asthma or early-stage chronic obstructive pulmonary disease), which cannot be directly visualized using current clinical methods, thereby motivating the experimental development needed for clinical translation. Finally, we discuss quantitative requirements on distances and X-ray source/detector specifications for clinical implementation of phase-contrast chest radiography.