Paupers would have a problem greater than their possession of money. I mean, money is a pretty good indicator of success or lack thereof. Not a perfect indicator by any means. For example, Jesus was not born into wealth nor did he acquire any but his impact on history is probably greater than any other single person. But I think you would agree that Jesus was an exception in every respect. Most poor folks are unexceptional in every respect.

But folks of means, but not great wealth, also get elected. Like Clinton, Nixon, Johnson, Eisenhower, Truman, Obama, Hoover, Lincoln, etc. A mixed bag. Wealthy people provide a mixed bag, too. Like the Bushes, Carter, Harding, Roosevelt(s), Washington.

It would be interesting to see a graph of historically successful presidents vs personal wealth. I haven't seen one but I'll bet it is inconclusive.