First, your premise is false:
https://en.wikipedia.org/wiki/Distribution_of_wealth#In_the_.... As of 2007, the top 1% owned 35% of wealth, while the next 19% owned 50%. The top 20% is a net worth of about $500,000 including home equity, which pretty much any household making $200,000 will as they get older. Moreover, the wealth of the top 20% is going to comprise to a much greater extent ownership of scarce resources (housing in desirable areas, etc.) than the paper wealth of the top 1%.
Second, what we care about at the end of the day is the distribution of access to consumption. Income models that better than wealth. Mark Zuckerberg might have an unrealized gain of $1 billion, but he can't out-compete someone else for access to scarce resources unless he realizes that gain. Indeed, Zuckerberg's wealth in particular is just a proxy for the right to receive a portion of Facebook's profits in the future based on the future labor of Facebook's employees. It doesn't represent anything tangible that exists right now. It's realized capital gains, not unrealized paper wealth, that is the proxy for goods and services that could be used to meet peoples' needs in the present.
Third, the folks paying "15%, 10%, or 0% in taxes" represent an extremely small portion of total income. Eliminating the preference for capital gains, for example, would raise just a couple of hundred billion more in taxes (compared to the almost $7 trillion we already raise). It's something that makes a few people very rich, but they don't account for a very large portion of overall income.
Fourth, and finally, someone making $200k/year isn't paying "close to 50%" of income in taxes. In Maryland, it's just over 30%. We're one of the few developed countries that taxes the top 5% so little.