You don't get the "best and brightest" with hereditary rule, though. You get those who are offspring of the current rulers, nothing more, nothing less.
Well, it's worth examining why hereditary rule happened basically everywhere. Obviously, rulers are nepotistic, but extremely common social structures generally had benefits for the majority of people. In the broad scheme of things (spread across hundreds of nations and thousands of years) social structures are subject to evolution. Social structures that inherently weaken the state tend to die out. Social structures that strengthen and make it more robust tend to survive.
When you look at history on that scale, common social features (like hereditary-rule, feudalism, monarchy, etc.) represent local maxima. Not "the BEST way to run things" but rather "BETTER than any easily transitionable structure."
Which brings me to my main concession to classic conservatives. If you don't understand the benefits of common, long-standing structures, you're not qualified to change them:
In the matter of reforming things, as distinct from deforming them, there is one plain and simple principle; a principle which will probably be called a paradox. There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it and says, "I don't see the use of this; let us clear it away." To which the more intelligent type of reformer will do well to answer: "If you don't see the use of it, I certainly won't let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it."
So what purpose does hereditary rule serve for a society? It's a structure that allows a society which cannot POSSIBLY afford public education to still train a small percentage of its scions from birth in governing and administrating. Sure, some of them lack the innate knack for it. But overall it increases the quality of administrators available in the society over non-hereditary rule.
That's also why we've evolved hereditary rule from an elective system. The previous rulers could afford to teach their children to rule, and rule efficiently. Which made them much more likely to be chosen as the next ruler. This process also increased the skill of our average rulers, and is partially why we rarely get BAD kings.
Edit: Amusingly, I've actually found myself in violation of Chesterton's principle regarding guilds. I CAN'T see what net good they provided to society... which is why I've stopped advocating against them. Obviously, I'm critically ignorant or biased in some way. I'm in the 'go away and think about it' stage...