There are two extreme ways to remove the inheritance problem. One would be to forfeit personal property: you can't give what you don't own. The other would be to remove the concept of family: when born you are placed in a communal system to be raised by professionals. People start with the same chances, the same level of social knowledge, network and vocabulary, you almost get to a pure meritocratic society (there are still those pesky genes).
Let's not imagine the unwanted effects and just bask in the idea of those kind of perfect societies.
Let's not imagine the unwanted effects and just bask in the idea of those kind of perfect societies.