Anarchists do not wish to abolish government, as much as they wish to include everyone in it. The state, being a centralized institution with a monopoly on legal violence in a given area, which has a governing body that controls it, is what anarchist want to abolish. aka, no monopoly on legal violence, no police. Police would be replaced with voluntary security forces, that wouldn't have coercive authority over anyone. As for inequality, I, as an Anarcho-communist, believe anarchism with markets can lead back to capitalism. I've read critiques of anarcho-mutualism, which is market based, talking about how the inequality between the competing collectives can cause a class system with elites that can have enough power to recreate wage labor, and by necessity, a state, to maintain private property. Private property should not be mistaken with personal possessions.. personal items you can justify having as means to directly enhance your living conditions. Private property would be like 100's of acres of land owned by a corporation.. The capitalist class would be abolished under anarchism, so to answer ur question about the 1%, if a revolution took place, and succeeded, the capitalist class, while maintaining their possessions, would have their production land collectivized.