Population aging has increased demand for walkable community healthcare for older adults. Using the six central districts of Nanjing as a case study, this study examines whether nominal 15 min access to community health service centers (CHSCs) translates into effective and equitable spatial access after accounting for pedestrian-network barriers, distance decay, and population competition. Based on the 2024 official CHSC roster (n = 60), a census-calibrated 100 m population grid, and an OpenStreetMap walking network, we computed walking times from 500 m hexagonal origins at 1.0 m/s. Binary coverage was compared with equal-supply Gaussian two-step floating catchment area accessibility, and population-weighted Lorenz–Gini measures were calculated overall and among covered older residents. Among 581,474 residents aged 65 years and older, only 28.1% could reach a CHSC within 15 min; 24.8% of covered residents fell below the first quartile of competition-adjusted accessibility. The weighted Gini coefficient was 0.861 overall and 0.506 among covered residents, and high-demand, low-effective areas contained 37.9% of the older population. Under the stated assumptions, the results indicate that nominal proximity overstates modeled equal-supply CHSC accessibility and that joint assessment of coverage, accessibility, conditional equity, and spatial typology can better screen areas for subsequent capacity audits, facility-siting assessment, or pedestrian-network improvement.