>>58226696I think of it as something in-between an international sports association and an academic body that holds weight in international politics. Each regional branch holds weight within and answers to a higher organizing body that sets standards of conduct and rules of competition, while also facilitating amenities such as Pokemon Centers, Poke Marts, etc. Additionally, they provide most of the grants and funding to Pokemon professors and researchers; any government-issued funding is pursued independently by such researchers for their own pet projects not already covered by the League's grants.
Regions that want to start up their own League have to go through both a rigorous application process that gauges the prestige, revenue and talent pool they might provide to the League, as well as hefty contributions to the League's finances to provide the complementary services that Trainers receive. This kickstarted flow of revenue is also how Champions, the Elite Four, and gym leaders and all their associated facilities are compensated.
Johto initially operated under the Indigo League due to its lack of proper funding to establish an independent League; in my fic, it took Ethan becoming independently wealthy and organizing heavy investment out of his own pocket to get a League of the region's own.
I suppose this also begs the question of whether there's a Great Champion representative of the overall League. 
