Unless everyone has exactly the same amount, it is mathematically necessary that the top N% percent will have more than N% of the wealth. The same reasoning can be applied iteratively within each wealth group.
Most people who write about wealth distribution on blogs or popular political sites and forums, or make videos about it, don't seem to understand this, and so fail to start with a reasonable model of what a fair wealth distribution would be.
While this is mathematically true, I don't think it is necessary to acknowledge it in order to suggest/discuss a reasonable model for wealth distribution. I would even say that it is beside the point. The OP is trying to show that the order of magnitude of US wealth (or income) inequality is shocking. Moreover, most of us vastly underestimate the magnitude of US wealth inequality. And I would add as an example that many still believe in the American Dream, even if the US is one of the worst OECD countries when it comes to social mobility [1]. As George Carlin was saying, "You have to be asleep to believe it."
Back to the OP, when the top 1% has 24% of income (and 40% of wealth), that means there's a lot of luxury in the US which could instead be used to improve the life of some other less fortunate citizens. The economics rhetoric is clearly failing: the current wealth distribution is certainly not the most efficient distribution of resources if one is to include "quality of life" in the equation.
It's easy to create that model: just take a time machine (or history books) and copy the same wealth distribution of America a few decades ago, say in the 1940's-1960's. Also known as, the Golden Age of the American Middle Classes. I would settle for that.
But that was a time when the very rich had to pay up to 91% of income tax, and unions were everywhere preventing exploitation of middle-class jobs! OMG, the US was a Socialist country, thanks god we don't have this problem anymore!!
(Sarcasm aside, yes the world has changed and the exact same formula that worked in the fifties wouldn't work perfectly in the modern and globalized economy; still, in this case the present is so screwed up that even an imperfectly-fit clone of the past would work better)
Most people who write about wealth distribution on blogs or popular political sites and forums, or make videos about it, don't seem to understand this, and so fail to start with a reasonable model of what a fair wealth distribution would be.