Why did the Founding Fathers prefer rule by the 'natural aristocracy in the
democracy they created?

To make sure that only competent people became leaders of the government.

Explanation:

James Madison define Natural Aristocracy as aristocrats who were selected by the the people in order to guide them to achieve common goods.

The founding fathers wanted United States to stay away from the monarchy stay. They wanted the citizens to be the one that hold the most power within the government.

They observed that Aristocrats from Great Britain obtained their title simply by birth. None of them have to earn the consent of the people. But, they have different plan for united states. They wanted the Aristocrats who govern this country should be someone with enough wisdom, virtues, and competency to  bring prosperity for the people.

if you are talking about current time the answer is no

if you are talking about when the colonies were developing the answer is yes

i think they came to washington to protest