Someone I know used to brag about the stunt he pulled to embarrass the private high school he went to and I shut him up pretty harshly about it because I had suffered so much in the public schools and how I would have appreciated the privilege that he got more than he did.
Of course he had his own problems including a struggle with alcoholism, getting beaten up by the cops, etc. and today he is a tenant and I am his landlord so it's not like I didn't catch some breaks.
I wasn't bullied by the other students, but I witnessed an incredible amount of racism to other students that was largely whistled under the carpet. The "vote Tory" banners under the school entrance every election day, the sheer theft of the school administration when it came to school uniforms, stationary, and simple things like paper.
And then the elitism. They tell you that you're special to be there, next world leaders in politics or industry or what have you. Of course, they don't mean you - they mean the hand-selected elites that served as prefects or head boys and other from purer backgrounds with the same grades as yours.
Uni was a breath of fresh air, like finally stepping out of the shadow of someone else's ego and never realising it until that moment.
Why wouldn't there be? Wouldn't safe, comfortable kids have less to win and more to lose from aggression?
As for taking to others bad home experiences, like mimicking an abusive parent, that can happen to rich as well as to poor kids...