Fastforward a few hundred years later, and the problem is well on its way to being fixed. The state tries its best to feed children as much as they need (though it fails miserably on several counts) and also to educate these children growing up (and again, tends to have decidedly mixed results) so that they can be useful members of society - if not at the upper echelons. In terms of intelligence and physical prowess among our youth, I think it's fairly safe to say that there's less of a divide between the rich and the poor than there was in medieval times.
But the big problem on the horizon is that education and nutrition are only the starting point. If you really want to improve your children's capacity for greatness, you'll engage in genetic engineering.
Intelligence, as a high level function, is going to be ridiculously difficult to engineer. Genetic engineering isn't all that sophisticated compared to where it will be in the end game, but that doesn't mean that we're not quickly approaching territory which used to be reserved for science fiction. In fact, the ability to engineer intelligence will most likely happen after human cloning becomes viable (especially if they lift the ban). Either way, once this happens, the divide between the rich and the poor will become even more pronounced, as rich children will be genetically superior to poor children, in addition to the host of other benefits they enjoy.
This is an interesting vision of the future that I don't think will come to pass. The big problem with extrapolating from current trends is that multiple trends happen at the same time. So while genetic engineering is moving fast, it's also competing with artificial intelligence and nanotechnology. Those three form the basic core of what's to be expected from the future, and they will all arrive into fullness in a series of quick steps that's already happening. So don't worry about the new aristocracy - worry about a million small things happening at once that will render this world unrecognizable.