Human abilities vary, and with them our degree of power. Physically, intellectually, economically, militarily and so on. You could define power as the ability to effectively pursue your goals. Said goals could be good or bad.
So you could look at the history of world War 2 (as the largest power conflict in history) and say that the axis powers were more powerful at one point, but then overreached themselves and the Allied powers were more powerful by the end of the conflict. Afterwards the allies fell out and there was a long power struggle between the major capitalist and communist powers with one side or the other holding the advantage at different times.
Ultimately it comes down to the fact that resources are limited and lifeforms compete for those resources with varying degrees of success. That sounds very abstract, but consider smallpox (a disease which only affects humans and no other animals); humans turned out to be more powerful, to the point of eliminating smallpox entirely, but before doing so, smallpox was a major threat to human life, killing hundreds of millions of people during the 20th century alone (about 5-10x as many as the total number killed in WW2). This is a fine thing from a human point of view, not so much from the point of view of the smallpox bacterium which will never get to discover its evolutionary potential. Being a human rather than a bacterium, I'm happy to be on the winning side of this particular conflict.
I do not believe that any economic or political system will result in total equality of outcomes, ever. Natural phenomena, including economics, obey what is known as a
power law distribution in which power (as a measure of energy) is inversely proportional to frequency (in this case I'm referring to specific power law distribution known as '1/f'). In economic terms, that means if we consider money as a form of spending power, there will always be a small number of entities who hold a large amount of money, and a much greater number of entities who hold a small amount of money (I say entities rather than people because states are economic entities too).
This doesn't mean that money is bad - money is just a method for counting the degree of economic power, in the same way that watts are used as a measure of electrical power. It provides us with a useful method of valuing different things, saving debate over questions like whether a pair of pants is worth more or less than a pair of shoes.
Now this distribution (a few very large things, a lot of very small things) shows up
throughout nature. It appears in galaxies. It explains why hydrogen (the lightest element) is also the most abundant in the universe. Waves. Earthquakes. Animals, both inside individual cells and as whole organisms (a few giant blue whales, a vast number of tiny bacteria). In economics it is often known as a
Pareto distribution (
http://en.wikipedia.org/wiki/Pareto_distribution - warning: math-heavy after the first few paragraphs). To quote the film
Pi, which discusses it in the context of pure mathematics, 'My new Hypothesis: If we're built from Spirals while living in a giant Spiral, then is it possible that everything we put our hands to is infused with the Spiral?'
In short, unequal distribution (of anything) is a
fundamental law of nature. It is literally woven into the fabric of the universe, the solar system, the land on our planet, our DNA, and everything we do. The evidence for this is overwhelming, and it finds its highest expression in mathematics - most famously in the distribution of prime numbers, which is a proven theorem. Note, please, that all these examples are dynamic systems: the exact configuration of any system (energy, mass, population, money, whatever) is in constant flux but remains very true to this power law distribution over time.
So while the biggest city in the world has changed numerous time throughout history, say, what remains the same is the fact it is about twice as large as the next biggest city (at any given time). If you aggregate the results of sports races (with everyone starting out from the same position), the finishing times will obey a power-law distribution. And so on.
To sum up, economic disparities are a reflection of the natural order. Nature does not go in for even distributions, it goes in for power law distributions. No matter what economic rules you implement, over time disparities will emerge that reflect a power law distribution. Not only will they occur across the system as a whole, they will occur within the components of that system. There is no need to engineer this: it emerges naturally, and inevitably, as a component of any dynamic system. We do not allow it: rather, we are powerless to prevent it. In any system that attempted to force an even distribution of wealth over time, more and more resources would have to be spent to prevent such disparities occurring, and the concentration of resources to achieve that end
would itself result in disparities of power.
This is exactly what happened in the USSR, where an attempt to enforce even wealth distribution resulted in an extremely authoritarian system where all power was concentrated in the hands of a very few people and the majority of the population exercised almost no political power at all. Like pushing down on a water bed, the attempt to smooth out economic disparities just gave rise to a political disparity instead. In the west, we go to considerable lengths to smooth out political disparities (in the sense that everyone has a single vote to 'spend' at the polling booth) but they still exist - one president, 100 senators, ~500 members of Congress, and correspondingly lower amounts of power at the state and municipal levels. It's possible that our attempts to establish total political equality actually increase economic disparities insofar as money can be converted into political influence.
Any attempt to engineer a uniformity of outcome is subject to interference from external factors and will come to resemble a game of whack-a-mole, and are thus more wasteful of resources than a purely competitive system. One might argue, then, that analysis of the Pareto distribution suggests that spending about 20% of our resources on governance will result in the greatest degree of freedom for about 80% of the people. Kindly note that this a conjecture on my part rather than a fully developed hypothesis.
I doubt that this is the answer you expected, or wanted. But I am pretty sure that it is the most truthful answer to your question.