AFTER THE MIAMI Heat drafted Dwyane Wade in 2003, he quickly deduced that the dopp kits his NBA teammates used to cart toiletries into the locker room telegraphed status. “If you had a Louis Vuitton dopp kit you were doing something,” he said. “All the older vets had that.” Then, as now, the French label’s immodest, $700-plus leather wash bags, often splashed with its logo, can rival a children’s shoebox in size. To a rookie guard like Mr. Wade, they practically shouted, “I’ve made it!” Wanting to hold his own in the hierarchy, he soon amassed an arsenal of luxury dopp kits. “You don’t want your toiletry bag to be busted,”...