The big idea here is that the current mix of haves and have-nots owes a lot to the ethically objectionable behavior of rulers and the politically connected in generations past. I don't think many would disagree with this.
Given this reality, we now must decide if we should do something about it, or do nothing.
The do-nothing approach is not very appealing at first. But we must be alert to the danger of the Politician's Syllogism:
Indeed, it is a businessman, a certain M. Le Gendre, to whom we owe our term for the Do Nothing philosophy. "When the eager mercantilist minister asked how the French state could be of service to the merchants and help promote their commerce, Le Gendre replied simply 'Laissez-nous faire.'"
Something must be done.
Here is something.
Therefore, it must be done.
My concern is that many commentators (and my fellow armchair commenters) advocate measures to correct the inequality problem using the same tool that Mr. Carson shows us is largely responsible for creating the problem. In order to pursue a political solution to the problem, concentrated political power is needed to effect the change. This power has been the source of the greatest harms ever caused by humans. Empowering an agency with resources and authority and a mission entails risk that the resources will be misused and the mission perverted. A discussion on guaranteed income points out some not-immediately-apparent difficulties in getting a result that is better than doing nothing.
Carson, citing Rothbard, argues for an "appropriate model" of privatization. It's not very clear how it would work, but the endpoint is still attractive: reduce the scope and power of the entity which now wields unprecedented power, claims authority in matters of life and death, and sometimes most worryingly, bumbles fearfully.
What, then, must we do nothing and simply live with the deplorable consequences of past injustices? I think there is a better path, and most of us are already on it. By working hard, producing and consuming, we contribute to the creation of wealth that has brought about the greatest improvement in welfare the world has ever seen. Obviously we who produce more enjoy more benefits, aided as we are by advantages both fair and unfair, compared to those in the lower half who get by on less than $10,000 in annual income. But, contrary to what some manifesto writers would have us believe, things are getting better for almost everybody. "The target of reducing extreme poverty rates by half was met five years ahead of the 2015 deadline."
My advice is that we work hard, produce what we have talent to produce, guard against the ennui that comes with an acquisitive middle-class lifestyle, and participate in charity whenever possible. I believe that if we are allowed to do that, we will see better outcomes than if we install minders to direct our behavior and tell us how to use our resources.