If all wealth were divided equally, that would mean ~$330K to every man, woman, and child in the country, and one would assume that means that all assets would have to be repurchased at an auction, which would give a huge advantage to big families, and that initial advantage would snowball the way initial advantages currently do. Theoretically annual income would also provide a big advantage, but people's incomes would be changed drastically as a result of the wealth reshuffling. My guess is that there would be very little correlation between pre-shuffle wealth and post-shuffle wealth. If we're just talking about cash shuffling, there probably wouldn't be that much of a change.
The general idea that wealth is mostly a result of wealth-acquisition skills seems way off, too. Remember that most Americans' net worth is mostly tied up in their houses. We're not generally talking about real-estate investors. People buy a house in the neighborhood where they want to live (near where they grew up or went to college or got a job), and they gradually pay it off, and in some cases, the values soar. Most millionaires fit that category. There's no reason to think they'd get the same results in a reshuffle situation. Incomes also are heavily dependent on luck (for example, people who enter the job market during a recession have permanently depressed incomes, while people who enter during a boom benefit for life on average), but there are skills that would be highly rewarded, and people who have them would always be financially successful (and I think that kind of urban professional types would gain a lot relative to the extremely rich or to people who inherited or work at high levels of family businesses).