Some of what you refer to in the lottery I don't see as privilege, such as genetics, when you live, it's the cards that you're dealt. It's the cards that everyone is dealt. You don't get to pick them. And some might confer privilege or destruction, such as who you know and where you live. The end is the same. We're here and then we're dust.
"Who you know" carries only so far, and if you can't earn the benefit, it will go away, just not necessarily with the same possibly catastrophic results for others with less resources. How about "who you are friends with". Is that privilege, and if so, what's wrong with that? Why is the notion of privilege necessarily a bad thing in and of itself? Isn't there the matter of context?
For example, I was elected to membership in the Academy of Television Arts and Sciences. While I haven't been nominated for an EMMY, several members asked me if they could sponsor me for membership, and after viewing my credits, a committee, none of whom I knew, voted unanimously to make me a member. That gives me the privilege of voting for EMMY awards and attending the EMMY ceremony. It allows me to watch all of the nominated programs on either the Academy site or through a special login to watch material on pretty much any streaming platform during the nominating period so that I can make an informed decision. It allows me to help talented college students to get internships. It does zip nothing to help me land a job. How is that a bad thing? I think it's kind of cool that my colleagues wanted to do this on my behalf.
As for divisions in the US? They're primarily driven by the twin gods of Fear and Grievance, historically very powerful forces. And because we have powerful tools for spreading Fear and Grievance, it's spread very efficiently, bathing everyone with its malign stink. Put out a statement, back it up with nothing or made up stuff and the majority of people will believe it without question. According to Pew Research, about 30% of the population gets its news from social media:
Social media plays a crucial role in Americans' news consumption, with about one-third of adults saying they regularly get news on Facebook and YouTube.
www.pewresearch.org
and that gets spread around to their friends. "I heard", "They're saying" are hardly hard data points.
Early in my career, I worked on hundreds of commercials and saw up front and close how powerfully persuasive suggestion works. The difference between 35, 40 years ago and today is that the methods of manipulating people are much more varied, but that's all.