Along with giant national corporations, we got giant national labor unions. And in the mid 20th century the corporations cut deals with the unions where they paid over market price for labor. Partly because the unions were monopolies.  Partly because, as components of oligopolies themselves, the corporations knew they could safely pass the cost on to their customers, because their competitors would have to as well.
Inequality has no limit when the cause is providing wealth to society (as opposed to zero-sum games)
And while it would probably be a good thing for the world if people who wanted to get rich switched from playing zero-sum games to creating wealth, that would not only not eliminate great variations in wealth, but might even exacerbate them. In a zero-sum game there is at least a limit to the upside. Plus a lot of the new startups would create new technology that further accelerated variation in productivity.
So if you made it impossible to get rich by creating wealth in your country, people who wanted to do that would just leave and do it somewhere else. Which would certainly get you a lower Gini coefficient, along with a lesson in being careful what you ask for.