I'd certainly argue that the tremendous disparity is impossible to have under purist capitalism and entirely free markets. Assuming your starting point is not where all societies actually start from (destitute masses and lavish rulers) but instead have everyone start out equally educated and wealthy. You also have to discount corruption of the state, which is another critical aspect to the extravagance of elite wealth.
In a natural economy from a flat start you have people funding the interests of those with entrepreneurial spirit to form businesses. Assuming you have some form of social organization where those with the means and wit cannot just inflict violence upon others to get what they want, what generally happens is that capitalists build industry to create goods everyone else wants, while paying others to work for them where they get more money from the labor than the worker gets in pay.
Naturally, the total wealth of the workers must decline while the capitalists profits rise. But the capitalists want more money, and the only way to really put their money to work is either internal investment in their own company, or funding the ventures of others. Rather than the base state group funding of an individuals venture, you have one or few wealthy sponsors funding new ventures.
That does mean that over time you get fewer and fewer capitalist entrepreneurs that are successful, because less money goes into making someone elses business dreams come true and more goes into making the established businesses stronger.
But in that natural capitalist market you cannot do many of the things modern American companies do to exploit markets and produce unnatural profits. All of which require the violence of the state to perform, which is why government is always a double edged sword - you need something to protect the people from violence in the first place, but that just gives the violence to an influencable, corruptable group, and money - especially concentrated - talks.
But it is much harder to get a monopoly in laissez faire system where you cannot use regulations and ordinance to block competition the way almost every major business in the US does. Be it (ab)use of the patent system, abuse of zoning, abuse of permits, abuse of straight up law, companies constantly goad politicians into giving them an unfair advantage.
In that free market if someone starts abusing their growing monopoly for profit it opens up infinite room for competition because the only barrier to entry to a goods or service market is the ability to produce it. That requires a whole economy of productive goods markets - but you can always fill the gap from the start wherever monopolies arise, and while you can have monopolies form, they cannot act against the market for long without opening up room for competition - they have to skirt the border where their goods and services cost just enough to disincentivize competition which means just below new-entry market rates, and that is after all extrinsic influencers outside price - business practices and ethics, employee retention and satisfaction, and general reputation. Look no further than Wal-Mart for an actual example of a business that competes at below market prices but loses significant business to its own awful reputation.
So my point is that while capitalists in a laissez faire system can perpetually concentrate wealth, it really cannot happen nearly as fast as it has in the last fifty years because you need regulation to capture markets as completely as so much of American enterprise has.