1. The desire to maximize personal capital and assets.
2. An individualistic mindset
3. The compounding effects of (1) and (2).
With all three, you get the current problem as described in the article. Suppose you removed (3), and somehow you could maximize assets, but upon death (or some other "big" event) all of your assets were given to the community. This would result in wealth not being concentrated. Here I'm also including the creation of foundations and other "charities", which in my view are just ways to keep your assets concentrated, and you have some tax advantages of doing so as well.
Say you removed (2). Wealth concentration without the desire to personally benefit from it would result inevitably in the helping of others, as a healthy, prosperous world would ultimately benefit you (though, again, its not the goal). After all, what's the point of money if it doesn't benefit you? You might as well make the world you live in better.
Without (1), you naturally would not see the problem described in the article.
So, what's the TLDR? Basically,
1. Create a culture where people don't need to be so prosperous themselves.
2. Encourage schemes that benefit everyone instead of someone.
3. Prevent the concentration of wealth, and all of its pseudo-forms (foundations, real estate, etc.)