You're ignoring heritable wealth. Personally I support a 100% estate tax above some small multiple of the median salary, so that the meritocratic element of society can flourish. This doesn't prevent the parents spending lavishly on their children whilst still alive, and might need some provisions to permit such spendings (for educational and other pursuits while still developing) to be secured in trust form in case of premature death.

Right now inheriting valuable property and other assets is an "honest" mechanism, but is not at all clearly fair.