There's nothing wrong with reasonable income inequality. When it's gotten to the point of an average CEO making 400x the average salary of his employees, there's most certainly a problem. Our current sh1tty economic situation is living proof of that problem.
Otherwise you would end up with a communist system, where everyone listens to the same music, looks the same, has no drive and only party members enjoy wealth. And that's an historic fact.
What you described is a totalitarian government, not a communist one.