Poverty is not merely the consequence of the greed of the rich; it is a political tool to marginalize whole segments of the population. As more and more of the population is marginalized, obviously, decision-making is increasingly going to be in the hands of fewer and fewer people, and it will be in the hands of people whose interests and world view differ radically from the masses.
A more equal distribution of wealth means more collective participation in decision-making, and this will inevitably undermine the privileges of the elite class. Poverty is ultimately about political exclusion, not just financial deprivation