Well there is a perspective and future I never would have thought of. Still, I doubt war and famine could ever really be eradicated and even if they were, I'm sure we'd soon find a way to mess the whole system up. Would be kind of cool to live in such a World for a short while though.
War and famine isn't too hard to stop but unfortunately, it will either require some kind of global revolution or a united authority. I'd say that the AI could provide a very logical authority that would be hard to argue with since, it will make near perfect sense and from our view, much more sense than a human could.