I think having boxes would be completely copying PO, but maybe adding their own type of quest depending on what type of pokemon you want to randomly get, the missions will be different or something. ;p
EDIT: I put some thought to it and maybe a quest combining the boxes and the vocation quest could be implemented:
Depending on which type of trainer you wanted to be you would go to it's npc, say "fire master npc", or "electric master npc", now based on the npc you chose, you would get different missions, and after you do all of them you would get the vocation you chose, say "fire trainer" or something, and you would get a random pokemon of the type of trainer you chose to be (growlithe, vulpix, etc).