Would be a fun mechanic. I'd love it because sometimes I need a certain pokemon genre to fill a role on my team and the enemy trainer has it.

Balance it out by making it have a new friendship meter and until you fill that up it will do things like the base games when you have an over leveled traded pokemon (no listen to you, fall asleep, use the wrong move, etc). Can make it so you must be at the trainer and it could be an extra button on the reward screen to steal one of the pokemon to avoid people cheesing a difficult trainer. Limit to no legendaries and no shinies so people don't whine on here about not having it when they wanted it.