It's a lovely idea, but that system will have to be enforced by a power structure... which will always tend to grant itself special privileges. And even before such corruption, without inherited wealth, there will still be entrenched institutions that control resources, and have a continuity of leadership, that will always be looking out for themselves and their in-group. It's just natural.

Define wealth in an exact manner.

Because rich people have both the power and motivation to define it in a manner in which they still win. Wealth can be education. Wealth can be contacts. Wealth can be properties. Wealth can be businesses. Wealth can be in other countries.