Proximity-based cities have attracted much attention in recent years. The 15-minute city, in particular, heralded a new vision for cities where essential services must be easily accessible. Despite its undoubted merit in stimulating discussion on new organisations of cities, the 15-minute city cannot be applicable everywhere, and its very definition raises a few concerns. Here, we tackle the feasibility and practicability of the '15-minute city' model in many cities worldwide. We provide a worldwide quantification of how close cities are to the ideal of the 15-minute city. To this end, we measure the accessibility times to resources and services, and we reveal strong heterogeneity of accessibility within and across cities, with a significant role played by local population densities. We provide an online platform (\href{whatif.sonycsl.it/15mincity}{whatif.sonycsl.it/15mincity}) to access and visualise accessibility scores for virtually all cities worldwide. The heterogeneity of accessibility within cities is one of the sources of inequality. We thus simulate how much a better redistribution of resources and services could heal inequity by keeping the same resources and services or by allowing for virtually infinite resources. We highlight pronounced discrepancies among cities in the minimum number of additional services needed to comply with the 15-minute city concept. We conclude that the proximity-based paradigm must be generalised to work on a wide range of local population densities. Finally, socio-economic and cultural factors should be included to shift from time-based to value-based cities.