The title gained popularity - not the poem. When Kipling wrote The White Man's Burden, advertising was an emerging profession, meaning people were grasping the power of a tag line (or what we now call "branding").
The White Man's Burden was the perfect foil for those with imperialist, colonialist, and corporatist ambitions . Oh how easy it was to pretend they were carrying a burden, rather than admit they were g-dless, murderous and greedy SOB-s.