The Gini index only measures wealth, not other forms of power; a system that does not focus on wealth as a means of accumulating power and favors is going to end up with less formal accumulation of wealth, but not necessarily less formal accumulation of power. The Gini index does not, for example, reflect such things as access to higher-quality goods and services, or the innumerable favors exploited by Soviet apparatchiks that would be replicated in capitalist societies by the expenditure of wealth.
The Gini index only measures wealth, not other forms of power; a system that does not focus on wealth as a means of accumulating power and favors is going to end up with less formal accumulation of wealth, but not necessarily less formal accumulation of power. The Gini index does not, for example, reflect such things as access to higher-quality goods and services, or the innumerable favors exploited by Soviet apparatchiks that would be replicated in capitalist societies by the expenditure of wealth.