PITY THE MEN’S DRESS SHOE, once an inescapable sight in Milan. Whether we’re talking about pointy-toed Ferragamo loafers or hand-painted brogues from an artisan outside of town whose workshop’s location a Milanese gent would guard as closely as his grandmother’s bolognese recipe, formal men’s shoes used to rule the streets—but no longer. Along the cobblestone corridors of Italy’s second-largest city, sneakers now abound, from the simple (Adidas Stan Smiths) to the sublime (rare Nikes) to the ridiculous (the pervasive Triple S “ugly sneaker” from Balenciaga). Mirroring the city’s embrace of rubber soles, designer sneakers...