> It is no one's moral imperative to punish themselves for being placed in a good situation.
Nobody is arguing this. People that implore others to examine their privilege don't do so to make people feel bad (although this may be a side effect of having a new perspective).
> Our differences and our circumstances conspire to make it so that not everyone has the exact same shot at success, but that's not the worst possible thing that could happen either.
That's the thing, privileged majority groups often enact or re-enforce policy or social attitudes that have the effect of keeping people not in that group from success. The call to examine one's privilege is so that members of the majority group recognize how their position and actions keeps other people from success. Note that by success I do not just mean financial success, but even being alive for members of some groups is a success based on the amount of violence they face.
> If you want to reduce unfair privilege I would recommend starting by helping those without it, instead of obligating those with it.
You cannot simply opt out of privilege. Privilege is just as much about how others view you as the social systems and institutions that back you over other groups of people. Also, people who are suffering from the systems and institutions do not want a hand out, they want to be free to have their own voices and agency, something that is hard to do when privileged groups continue to undermine their attempts at that agency.