Good observation. I doubt she would have denied him the study of philosophy if they'd had Nietzsche, but as it was the philosophy he would have studied would've been Stoicism.
Your post brings up an interesting question: what kind of education should Caesar have? It would seem that the question would be particularly important in America, since, in theory at least, everyone takes up part of Caesar's role, but I haven't seen much discussion of it. Our education usually turns out worker bees instead. Critics of the education system usually talk about being prepared to get good jobs. That's important, of course, because you've got to eat, but that can't be all of it. Beefing up civics won't be enough either, because an educated citizen needs more than the ability to recite the three branches of government.
I had a look back at the Cicero thread just after posting this one, and something caught my eye that hadn't earlier. "Chiltown", which struck me as more utopian(in the good sense) than any of the political utopias, from Plato to Marx. I'm reading the Republic now, and in some ways it was like Socrates' first ideal city, which was rejected by his companions, in that it's a place for actual people, where the pleasures are ones that people can actually enjoy, not a happy city of unhappy men. I don't know if it's relevant to anything, it just struck me.