I suspect that a major factor driving envy of the rich is a deep-seated male fear of losing the mating game. My hypothesis is that the irrational resentment that many men feel over the high pay of CEO's and others can be traced to a deep-seated fear that some other man will wind up with more than his share of mates, and the rest of us will be left with none.
Then why are men's attitudes markedly less egalitarian than women's? This readily pops out of the General Social Survey, and has been explored at length in the literature on Social Dominance Orientation.
In any case, the idea that polygamy would destroy social peace is pure paranoia. If polygamy were common, there might be a marginal increase in crime, but it's hardly clear. Men might just work harder to attract a wife.
But more to the point, polygamy isn't going to become common even if you legalize it, because very few modern women would put up with it. In practice, polygamy would probably be about as prevalent as gay marriage. So why can't we just show some tolerance instead of predicting the sky will fall?