I think you guys don't understand the scope of Nemona's battle autism. When Nemona arrives to Kitakami she's always with Arven and Penny and they follow you to Kieran house. Then, she and Kieran run to the center of the town for a battle. After the battle, Nemona says she has to touch her team a little, seeing Kieran's level, but you all have to return to Kieran's house to nurse Carmine. Finally, the five of you unpack your stuff, and Nemona disappears, returning with some sodas from Peachy's (which is just next to your place), and she will later run to the Kitakami hall in a trance she won't even remember.
Despite this, when you finally encounter her in the lousy three's park, she has gotten herself a Kommo-o and a Rimbombee/Milotic/Dusknoir, all with levels in the 80s, all found in zones far away from your place, all caught and trained in one afternoon because she simply couldn't help herself seeing so many new pokemon.
Likewise, inviting her to BB Academy has her catching and training a Rowlet/Froakie/Chimchar in the terrarium before challenging you to another battle.

The world is lucky the MC is here to keep her in check, she couldn't be stopped otherwise. Her battle autism is just too strong.