I don't disagree with your points but I think you're just clarifying the question. The issue here is what to do with those problems and whether it is moral for the Government to forcibly remove wealth from people and give it to other people based solely on the fact that the people receiving the wealth think it's unfair they have less money.

It is "fairness of opportunity" vs "fairness of result". Or maybe more to the point "if we can't yet guarantee fairness of opportunity are we then justified in equaling out the result"