First, I think OP should edit the eradicate in his title pose to either ameliorate/curtail or reduced, give it a soft landing because it can not be eradicated in any society. And, if I have to make inference from the bible, do we still remember the rich man and the poor man story?
There are a lot of wrong statements in your post. A lot of wealthy people worked hard for that wealth, and no luck was involved.
I think that there is also the place of luck in our lives and being rich. The difference is that, being ready to identify the luck; in which case, the rich could have been ready. Off course, when being ready/opportunity meets luck, it takes one to wealth.
So we have to live ready.