The rich are not at fault by virtue of their wealth alone, but the way they accumulated it (and how they use it). The worst offenders would be the rentier class... which includes everyone from two-bit patent trolls to Monsanto, from slumlords to Donald Trump. These people extract unearned rent through the proxy of government coercion, and seek to monopolize the use of land, ideas, genes, and so on. They hold no natural right to do so, nor does this illegitimate form of property benefit society... indeed it actively harms society.
After that, the limited liability corporate person is the legal construct which promotes the greatest degree of centralization. It is this which allows leveraged banks and insurance companies the ability to go under while the investors can walk away without any liability for their reckless behavior. It is this which allows corporations to take ridiculous risks and create enormous externalities, safe in the knowledge that their investors would never be personally liable (think of the BP oil spill).
Then beyond that we are inflicted with all the centralization-promoting public transportation grids, communication grids, government-granted energy monopolies, agribusiness subsidies, etc etc etc. When you add it all up, and also throw in the history of colonialism and feudalism out of which our system evolved, and the ongoing imperialism being employed to maintain it, we can safely assume that virtually all of the elites have achieved their status illegitimately by any standard of either natural rights or common decency.
So yes, I did use the convenient shorthand of income inequality to illustrate how imbalanced things are, and by speaking of income in general I wasn't as precise as I could have been, but ultimately that income stems from the sources outlined above. This economic inequality then creates a huge imbalance in political power in which the rest of society has a very hard time competing, given the collective action problem, and it becomes very hard to change any of it. Even if we do live in an oh-so-complex world in which the politicians are often well-meaning and somewhat accountable to a multiplicity of factions, they still have to play the game... and that game is rigged.
It is for these reasons why it is perfectly legitimate to refer to the corporate-state apparatus as such.
Is the unequal distribution of wealth really problematic if the median household income and wealth increases at a constant, and relative to other OECD economies, at a historically healthy and competitive rate (keeping in mind the distortions created by the recent cyclical downturn)?
The recent downturn was hardly just "cyclical." It was the result of an unsustainable multi decade transfer of wealth from all of society towards the top 1 percent which started in the 80s, was vigorously supported under Clinton, and was intensified further under Bush II. In the context of a highly regulated economy, it is lunacy to open the floodgates to financialization of the economy, mergers of commercial and investment banks, persistent low interest rates, etc. There was nothing cyclical about that.
And if you want evidence of the political persuasion of the wealthy, look at the voting patterns of households earning above 200,000, or 350,000 annually, most of whom express a preference for Democratic candidates.
This is mostly a recent phenomenon, since Bush was such a disaster in every way that even the super-rich had turned against the GOP. Though that is just a temporary anomaly, and even if it weren't that would merely mean we are ruled by a smarter elite who are willing to appease the lower classes enough to ensure the most stable fiscal climate for their thievery.