Hmm, maybe the Gym leaders, but beyond getting badges and money, I'd argue that they're... pretty tame from a competitive standpoint. Besides, as far as they're concerned, all trainers should compete with each other.

They were doing it before we got here.

[So it's not like they're fighting over resources, right? Well, maybe if the local trainers bought up all the healing items, balls, or other gear, but the supplies seem pretty generous overall.]