Why not? There's plenty of people arguing for exactly that mechanism when it's not about their own children. A 100% inheritance tax (with no loopholes through business or legal constructs) might force a lot of people to rethink how they vote -- because then, they can't use their wealth to shield their children from how society functions any more.

If someone else's child was run over and killed in a road, a person may pause to reflect on how sad and unfortunate the event was, but will quickly move on with their life and continue as they were. If their own child though was run over and killed though, they would be shattered, may not even be able to function well for quite some time.

As such, your suggestion is quite literally against human nature. We're not insects. This is the usual trap for people with Big Ideologies: they assume that we're all these tabula rasa entities onto which anything might be written (and should be).

Literally the whole premise on which the plot of Inception rests was to convince the child progeny of wealth to forgo it so as to prove that he could make a name for himself on his own merit and not by riding his father's coattails.

There's a very big difference between leaving a child to fend for himself (so to speak) and attempting to help a child develop his own sense of agency, including restricting access to a smaller-than-naturally-limited set of resources.