>>13447730I imagine gym leaders are around the same level as the E4 and even the Champ. The League probably approves trainers for the position of Gym leader as well as E4 and champ, since each role involves something else.
The champ after all, is always shown to be traveling around on all sorts of business, the E4 probably do something along the same lines.
If someone choose to say rooted to on city, like for example Skyla, since she has the airport to take care of, ask to be given a gym instead.
Gym leaders most likely serve a purpose in their community, like helping trainers in their area improve and the like. Who knows, maybe your character in game is simply lucky to live close to a PokeProf as to get starters from them, gym leader might do the same thing for other trainers.
As for OP's pic, they most likely have a pre-approved roster for trainers of different levels.