I think there should be bullying in the Sims 4. It is a real life thing, and would really fit. The Bullier As the Bullier, you get to bully people. Steal their lunch money, pick on, yada yad...
I think bullying interactions are already in the game, sims can use the 'insult,mock,etc.' interaction. There's no need for sims to be defined as a bully or a victim because in real life you're not categorized by if you've been bullied or if you are a bully.