If heirs get money by virtue of birth and not value provision under most any system, and capitalism is among them, then capitalism isn’t a system which distributes money purely by value production.
So in your ideal scenario, rich people lose the privilege of being able to provide opportunities for their children? Purely because they are rich?
Even if you can walk it back from the edge of that cliff by saying they should have to provide for everyones' children, they can only do that by being rich...