By ignoring "lucky money", she creates a logical loop in which money becomes a marker for productivity. The more money you have, obviously the more productive you are, because there are no productive poor.
It is also the problem of equating money with wealth. Money is just a good faith token between parties to expand the barter system to people who would otherwise have no basis to barter. For example, I am a software developer. I need a plumber. The plumber does not need software developed. Now, I can initiate a whole chain of exchanges that winds up with me having something the plumber wants, but that is inconvenient for day to day living. To short circuit all of that I give him a number of markers equal to the value we place on his time.
The markers aren't the point. That's the problem we have. We are emphasizing these markers and ignoring actual production. In a true idealized society based upon actual utility and such as Rand would have it, it would not be the scientists, artists, and executives at the top of the heap, but the electricians, plumbers, carpenters, and other doers and makers as they possess the skills of making.
Atlas shrugged is just CEO porn.