There have been, historically and presently, power and wealth grabs by the already powerful, and manipulation of political and social structures to suit their needs. To some extent this was easier historically, partly because there were fewer laws, but even now, with the legacy of hundreds of years of social and political reform, and a lot of it intended to liberate common people, there are still large distortions in our political systems that significantly mis-allocate power to the already powerful.
I would also take some umbrage with your statement that we "haven't yet found a way to fairly spread privilege in our societies" and your defence of the "least worst system" meme. Whilst there are aspects of the Western socio-political setup that are designed around the (reasonably) fair distribution of wealth, there remains constant pressure against legislation designed to develop the rights of common people in society. Indeed, those interested in reducing those rights are often able to gain popular support for their cause by positioning themselves as defenders of the wealth and power of those people whose wealth has recently increased - i.e. the middle classes, which now form a very significant political power base.
We do know of ways of more fairly distributing the rewards of labour (cooperatives come to mind, as a single example), but they are unpopular in a lot of the West, and if you look back to history you will see that that mentality was actively created to counter threats to vested interests. Ironically the system of laissez-faire capitalism that was adopted to counter these more de-centralised power structures ended up diluting the power base of the "old money" (and was eventually massively scaled back), though it persisted the fundamental inequality in wealth distribution.
I would, however, fully agree with your assertion that these problems are not (or at least very unlikely to be) the result of a direct conspiracy by some elite group. I don't think history supports that view, and I don't believe people are particularly capable of maintaining such a conspiracy for so long a period of time. It should be clear, however, that the "conspiracy" could itself be an emergent part of the system - a higher order structure that has managed to persist itself (thus far) without continuous direct human intervention, however that would make it not a conspiracy in the traditional sense of the word.
N.B. This is obviously a pretty broad sweep based on my interpretation of history - if anyone has any corrections or comments I'd appreciate hearing them.