Dave, perhaps I am not following you correctly, but what you write seems to conscript Jesus's story of the rich man and Lazarus for the purpose of condemning a particular economic system you wish to condemn. On the other hand, I think it will condemn the elements of any "system" that do not agree with God's principles. Further, I don't think any one system has a corner on the market of getting it all right or all wrong. I'm no expert on economics, but some elements of trickle down seem to be beneficial. I worked for a building contractor for 15 years, starting when I was a teenager. He wasn't rich, but compared to me, he had a business, a home, and a farm (none of which I had), and a fair degree of prosperity. When his business did well, it "trickled-down" to me. For example, if he had lots of work, we might be able to go to another job inside when we got rained out, rather than going home. It might take the form of a raise. On particularly good years, we in turn received particularly good Christmas "bonuses" For example, he might pay us for the week and give us the week off. On the other hand, if the year wasn't good, the Christmas "bonus" would also not be as good. This was something "trickling down" -- certainly in a simplified form in which I can understand it, but an example of how it can be a good thing.
If there is a "system" in the story of the rich man and Lazarus, wouldn't it be the economic "system" of the law and religion of the Jews (at least to extent it operated under the Roman rule)? This system required its subjects to care for the poor (e.g. Leviticus 19:9–10; Deuteronomy 15:7,11; Deuteronomy 24:19–22). The law and religion of the rich man required him to "open his hand wide" to the poor, yet he let Lazarus languish at his doorstep. Ultimately, it was not a systemic fault, but a character flaw. The system wasn't the problem, the heart was.