You do note that nobody "dies" in Bully..They just fade away -- But shooting them and blowing up your characters are a sure way to decimate the school population quickly, not to mention the Town(s) and all over the enviroment of the "world" game limits....
When I first played Bully, I was really wanked off that I couldn't "kill" anyone -- So used to "Resident Evil" and "Manhunt" games, where you leave no survivors as you move along...But as I went along in the game, it made sense not to "kill" anyone......
In other games, you move...from room to room, building to building, street to street, even town to town, many of those never to go back....But in Bully, you stay in the same locale, interacting with characters sorta like real life....That, I believe, is the allure of the game, sets it apart, makes it different....Hell, even the Cops don't have guns (Even though one says "I've got something like that, only mine shoots bullets"), so the point of Bully is not to kill, just to give them a good ass-whipping....
All this said, however, I do like your Ideas, Mike....Perhaps a College Bully, where Jimmy lives a double-life, student by day, Gang Hitman by night, or just a Street Bully, where Jimmy would have to belong to a Gang (or not), and fight to kill......