Correct. I'd even argue that structure in the ideal sense is more akin to a house than to a toolkit. Less a direct way of getting things done, and more securing (or insulating) people from others so that they may get things done.

Mitigate or incorporate?

- "We seem to have a problem with people seeking power and privilege for their own gain." - "To prevent it, we should let some people exercise power over others in high-status positions."

Well ideally the corporate hierarchy should be deliberately constructed to put suitable people (skilled, fair, benevolent) in positions of power, and so should be superior to ad-hoc power structures arranged purely based on personal ability to manipulate social situations. Of course, that doesn't always happen...

Why not both?

IE, Firefighters will stop the spread of fires by setting controlled fires.