These days, I think most of the motivation to be seriously rich (vs. mere "can afford two nicer McMansions, and your kids don't qualify for college financial aid" rich) is a humans-are-primates obsession* with being further up the pecking order.

But your bottom line is still valid. The rich are definitely not allocating resources in ways which are beneficial to society.

*Less-flattering terms, perhaps from the DSM-5, would seem applicable in many cases.