You're getting plutocracy backwards. A plutocracy is a system where being rich gets you political power/influence.

For example, a millionaire can bribe an official or use his campaign/PAC contributions to convince them to do what he wants.

People getting rich because of political power is totally separate and will pretty much always happen because they get more famous and respected due to their power.

In short, plutocracy means money gets you political power, not vice versa.