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fubarobfusco comments on Harry Potter and the Methods of Rationality discussion thread, part 17, chapter 86 - Less Wrong Discussion
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No — they simply have not chosen to prove themselves to Harry, the viewpoint character.
I expect we'll find, soon, that Harry's model is wildly out of whack — adult wizards are, by and large, competent but flawed, especially the leaders and heroes. They simply do not let on to children everything they can do, nor their level of control over the world. Why? Because gifted children are not really all that rare, and teaching kids more magic than they are responsible enough to cope with is how you get Dark Lords — and dead kids.
Expanding on this — The purpose of magical education (e.g. Hogwarts) is not to teach kids as much magic as possible, to enable them to fix the world as Harry wants to do. The purpose of magical education is to safely and gradually expose them to magic, to maintain the current status quo and certainly to prevent any dumbass kids from destroying the world or killing each other. It also includes giving them chances to prove themselves responsible and skilled enough to wield more, and to put them in touch with adult wizards who might choose to individually teach more. But none of this is served by powerful wizards flaunting their top abilities in blatant and imitable fashion in front of the kiddies.
Nothing stays secret from teenage kids for long. No conspiracy of a large size can be maintained for very long (especially if it must admit everyone). And the Lucius Malfoys of the world would want to give their kids every advantage.
Parents in the real world want to give their kids every advantage too, but few sign their kids up for calculus class and gun-range time at age 6, you know? Parental conspiracies aimed at preteen children are remarkably resilient things(cf. Santa Claus). Teenagers are harder, but you can rely on most of them not actually wanting to be bothered learning any more than they have to.
Did Draco know about the Secret of Potions?
Did Lucius?
I got the impression it was common knowledge among powerful wizards. Am I misremembering?
If you look back at Chapter 78, it says that
Harry had not made an original magical discovery, but rediscovered a law so ancient that nobody knew who had first formulated it:
A potion spends that which is invested in the creation of its ingredients.
But conversely, it also says that
The fundamental principle of Potions-Making had no name and no standard phrasing, since then you might be tempted to write it down.
McGonagall and Flitwick seemed to at least be familiar with the idea, though, so there's a good chance that you're right.
Edit: I should probably also point out the obvious. If knowing the general rule is "WTF? Stop!" dangerous, like the professors seem to suggest it is when Harry tries it, then it's not generally the sort of thing you'd teach your 11 year old son. There's plenty of time to pass things like that along when the kid's closer to adulthood and mellowed out a bit.
Sure, that's why this is a story written by Eliezer and not (say) Piers Anthony. But still, an educational system does not last for long if it obviously gives every kid a nuclear bomb.
Well, that's true, at least.