IIRC from the Pokemon days, there were a lot of concerns around the ‘prize’ scoring system, with the idea that you’d take the opponent’s prize cards when you knocked out a Pokemon. Misunderstanding/holdover from Pogs, I think (where getting the other player’s pogs was a thing).

Couple that plus stories of kids getting knifed over holo Charizards, and I kinda get why schools were concerned (putting aside the ‘that’s not how the game works’ + ‘that was one psycho kid’ elements).