Complex, self-organizing networks necessarily create conditions of "inequality."
In a living cell, there are many, many, many more water molecules than there are DNA molecules. Yet the DNA molecules are by far the largest molecules in the cell, and they are the most important (per individual molecule). Yes, one must have water to have a living cell, but one can have water without a living cell. To have a living cell, you need large biomolecules, and large biomolecules will, eventually, give you a living cell as they interact with each other. Still, without DNA, the cell will eventually succumb to entropy and fall apart.
In an ecosystem, there are many, many, many insects, especially social insects like ants and termites. The larger the animal (or plant) in the ecosystem, the fewer there typically are. The African savannah, for example, has relatively few elephants compared to antelope (let alone ants or termites). There are fewer baobab trees than grass. It would be downright silly to complain that the baobab trees are larger than the grass and that that is unfair to the grass. Get rid of the baobab trees, and a great deal of the ecosystem network will collapse. The same is, of course, true if you get rid of the grass.
Human social systems are similarly structured.
Take literary production, for example. There are many people who are very popular for a short period of time, but few who are popular for a long period of time. There are many more Grishams than Shakespeares. And there are, of course, many more unknown writers than known writers. The best-known writers are the rarest, with moderately-known writers having greater numbers, and unknown writers having the greatest numbers. Is it "fair" that Shakespeare is extremely well-known around the world, but my plays are not? Would we really want us equalized?
What is occurring in all of these cases is the creation of what are called power laws. There are power laws of size, longevity, and influence in any self-organizing network process. Shakespeare is "wealthier" than me as a playwright because he has more links than do I. And the more people know of him, the more he is read, leading to him being better known and influencing more people, leading people to read him even more. My influence is, to say the least, less. If I influenced one person, I'm lucky to have done so.
Wealth in the market economy works the same way. Some people engage in more market interactions than others. The more one engages in market interactions, the more others want to engage in market interactions with you. Trust grows, riches grow, and thus wealth grows. As a result, we will necessarily always get disparities in income and in riches and wealth. In the market, though, one is made wealthier by providing others with valuable goods or services (including labor).
Wealth in the political economy also works this way. There is power-wealth, of course (the President has more power than does a given Senator, who has more power than a given Representative, etc.), but in an economy in which the government is involved, government can also affect distribution of money. Regulations will result in different patterns of riches-distribution and income. So, too, will favors and cronyism, etc. As a result, one would expect there to be a power law distribution of politically-influenced money-based wealth in an interventionist, regulated economy.
In other words, one simply cannot expect a government to equalize wealth/riches/money distribution. All it will do is distribute the money differently than would the market, but also in a power law distribution. In the case of the market, money will be distributed according to who provides the most value, as determined by subjective value preferences averaged out through the market. In the case of the government, money will be distributed according to who provides the most political support to politicians. The former creates more wealth for everyone, while the latter actually destroys wealth through its redistributions (in networks, manually redistributing the network links weakens the network as a whole, and can lead to network collapse -- all of which is to say, it makes the network less wealthy and less healthy). In neither case will you get any actual equality of wealth distribution. But only in the former case will everyone be better off from the way the network emerges.