Is there a correlation between capitalism and income inequality?

A large portion of inequality is due to the "Superstar Effect"

Question: Is there a correlation between capitalism and income inequality?
Position‹2 of 3›: Yes, capitalism causes inequality
Argument1 of 2›: A large portion of inequality is due to the "Superstar Effect"

The "Superstar Hypothesis" largely explains the inequalities seen today within the age of technological advancement, capitalism a driving factor in the emergence of the few over the many.

The argument

The "Superstar Hypothesis," first proposed by Eric Posner and Glen Weyl, basically claims that capitalism is inherently designed to benefit the few over the many because it is a system based upon a one-in-a-million talent. The mechanism is not corruption or rigged rules but the ordinary operation of a market in which buyers can all choose the same seller. It can be seen in sports, the music industry, and other forms of entertainment across the board, fields where audiences are free to attend to whoever is best and generally do. The distributional consequence follows from the scarcity of that top tier. Because there are so few "superstars" that naturally outperform their competitors within the market, their talent accrues most of the wealth for themselves. A small difference in ability at the top translates into a very large difference in reward, because nothing limits how many people can choose the same performer, and the runner-up is not compensated for having been nearly as good. The second-order effect is what the argument treats as the real harm. This, in turn, causes huge problems with inequality once those at the top are so few and far between that it is almost impossible to inspire economic incentive in people at the bottom or in the middle who are not economic superstars. A system justified by the incentives it creates stops creating them for most participants once the reward is concentrated in so few hands. The New York Times puts the point in terms of the calculation an ordinary worker makes: "If only a very lucky few can aspire to a big reward, most workers are likely to conclude that it is not worth the effort to try. The odds aren't on their side." Because the effect is structural rather than incidental, most detractors of capitalism claim that we must curb the "superstar effect" through governmental intervention.

Premises

[P1]The 'Superstar Hypothesis' holds that capitalism rewards a tiny number of one-in-a-million talents who accrue most of the wealth. [P2] As wealth concentrates among these few superstars, it becomes nearly impossible to inspire economic incentive in everyone else. [P3] Most people conclude the effort isn't worth it when only a lucky few can win big. [C] Therefore, because a large portion of inequality stems from this superstar effect, capitalism causes inequality.

Counter-arguments

The "Superstar" effect is not necessarily bad, nor is it a natural indication that inequality will exist in a positive feedback loop forever. In a free society, the most gifted and talented should be able to reap the benefits of the system without being stifled by governmental forces. The lack of technological innovation and progression into the future that would result from such a leveling of the talent pool playing field would drastically change society in a plethora of negative ways. Incentivization, rather than simply decreasing over time, would be completely non-existent, and everyone would shrink to the bottom without a goal.

Rejecting the premises

[Rejecting P2] Taking away the "superstar effect" would completely decentivize any individual need for personal growth or the overall technological advancement of future society. [Rejecting P3] The "superstar effect" should not automatically be curtailed.