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No. Adults in the pokemon world typically have too many other responsibilities to be traveling around constantly battling and improving their skills or meeting new pokemon. That's why gym challengers are typically young and even most gym leaders are young adults, at best.
The handful that stay professional trainers even at an adult age hit the plateau pretty quickly because they start slowing down well before their Pokemon do. That's why they take static jobs like Gym Leaders or E4 members.
