However, the spells they do cast are fully as powerful as those of adults with wands.

In fact more powerful than most adults; there's a line in Chapter 78 that "If [Mr and Mrs Davis]'d been children young enough for accidental magic they probably would've spontaneously Disillusioned themselves.", which we know requires significantly above-average power in MoR. (Assuming that line from the narrator isn't exaggeration.)

Otherwise your hypothesis is credible, though I still don't accept it as I can't see all the high-level wizards we know being dependent on wands when there are so many advantages to wandless magic

If you accept the hypothesis, wanded magic has the not-insignificant advantage of being more powerful. What's the advantage of wandless magic?

Muggle America is also some hundreds of thousands of times more populous than wizarding Britain. That does change some things when it comes to ratios of that sort.

it takes several casters

Several first-year casters. Quirrell stuck 50 people to the ceiling. You might say that he has better ways to use his power - but the killing curse is not one of them. His killing curse is little better than anyone else's.

Also, it seems unlikely at best that the Hover Charm can accelerate people downwards

There's got to be a spell for that, and it it likely to work similarly to the hover charm, i.e. instant effect.

Also, it's possible that the Hover Charm could be blocked by a pre-cast shield

If by a specific anti-hover shield, then one needs to always keep up a large number of shields against various spells. If by a generic shield, well, that isn't in my mental model of shields, but I guess it's possible. In which case I agree that the killing curse is superior agains a raised shield, but it is still inferior against an unsuspecting enemy.

You're right, no hint of an explanation why wands are necessary has ever been given. Spontaneous underage magic, as well as high-level wandless magic, would be evidence in favour of the "conceptual limitation" theory.

On the other hand, this wouldn't explain why Bacon, who apparently lacked this conceptual limitation, was severely held back in his research by lack of a wand. Also, it doesn't explain why high-level wizards continue to use wands for the overwhelming majority of their spellcasting.

A matter with the Comed-Tea that was bugging me for a while:

Chapter 14:

SO THAT'S HOW THE COMED-TEA WORKS! Of course! The spell doesn't force funny events to happen, it just makes you feel an impulse to drink right before funny things are going to happen anyway!

Hypotheses: Comed-Tea on person = impulse to drink, Comed-Tea not on person = no impulse to drink.

According to Chapter 12:

Harry couldn't help but feel the urge to drink another Comed-Tea. (And when he didn't...) Harry inhaled his own saliva and went into a coughing fit just as all eyes turned toward him.

So no matter what, even if you don't end up drinking it, you will get the Impulse before something funny happens.

Chapter 46:

I have been saving them for special occasions; there is a minor enchantment on them to ensure they are drunk at the right time. This is the last of my supply, but I do not think there will ever come a finer occasion.

So Harry has used up all of his Comed-Tea. (edit: it appears that Harry actually has tons left unless he's not mentioning some he drank/gave away, look at bottom of post)

...

WHY? WHYYY?!

It is apparent that you'll still get the impulse to drink whether or not you do end up drinking. So why didn't he save a can he's never ever going to drink?

Even if Harry will end up choking on his saliva, wouldn't the early notification of something ridiculous happening be helpful to him in any way? Like... it'd be an early warning to be prepared for whatever another person could say/do in conversation. Or if he's looking for interesting information, say from the library, he can just walk by all the shelves until he gets the Impulse-- that'd be an indicator that he's near the shelf that has the interesting book. There might be more uses.

Chapter 14:

Thankfully, Harry’s panicking brain remembered at this point that he did have something he’d been planning to discuss with Professor McGonagall. Something important and well worth her time. It was at this point that Harry realized he was faced with a priceless and possibly irreplaceable opportunity to offer Professor McGonagall a Comed-Tea and he couldn’t believe he was seriously thinking that and it would be fine the soda would vanish after a few seconds and he told that part of himself to shut up.

The charm even works for other people. If, for example, Harry wishes to test whether or not someone knows that Voldemort is alive, he could see if he has the Impulse to give that person a drink, all while thinking about saying that "The Dark Lord is still alive". If he gets the Impulse, they don't know. If he doesn't, then they already know/has been suspecting that he's been alive.

Chapter 8:

The boy reached into his pouch and said, "can of soda", retrieving a bright green cylinder. He held it out to her and said, "Can I offer you something to drink?"

Hermione politely accepted the soda. In fact she was feeling sort of thirsty by now.

In fact, just asking, "Are you feeling thirsty?" seems to be enough to trigger the charm's apparent spit-taking powers. Harry could think about talking about Voldemort, and ask if the other person's thirsty. If yes, they would take whatever he's going to say as a surprise, if no, then they won't. Geebus this thing is powerful.

edit: actually, I'm going to check the text and see Harry actually used up his supply. Be right back.

Chapter 7: “Two dozen cans please.” (24) He tossed a can to Draco and then started feeding his pouch... (23) (Harry's drinking one too) (22) Harry snarled, threw the can violently into a nearby garbage can, and talked back over to the vendor. “One copy of The Quibbler, please.” He paid over four more Knuts, retrieved another can of Comed-Tea from his pouch... (21)

Chapter 8: The boy reached into his pouch and said, “can of soda”, retrieving a bright green cylinder. He held it out to her and said, “Can I offer you something to drink?” (20)

Chapter 12: Harry reached into his pouch and whispered, “Comed-Tea”. (19)

Chapter 46: “Three sodas." (16)

Nevermind, Harry lied, he still has tons unless he's been drinking them and not mentioning it. However the Comed-Tea hasn't been mentioned since, so it might actually be all gone.

I wasn't aware that Draco was an Occlumens. (If he can't beat Veritaserum, those promises mean precisely nothing.)

Lucius didn't ask if Harry could cast a Patronus, I could buy that. But Draco's Patronus didn't come up? Harry's vow of vengeance against Narcissa's killer didn't come up? That whole thing was possibly the single most important interaction Draco and Harry have had, next to when Harry tricked Draco into sacrificing his belief in blood purity.

Five days was too long, IMO. If we only had 24 hours I would have enjoyed it much more.

How do you propose organizing a 'master list' of solutions, relevant plot pieces, etc. given the current forum format? Some people have made some lists, but they are often quickly buried beneath other comments. I'm also not familiar enough with how things work to know if a post can be edited days after it has been posted. One obvious solution is that a HPMOR reader who likes making webpages puts up wiki page for this. Can this be done on Lesswrong.com?

In retrospect, our guesswork was a lot messier than it should have been.

Chapter 25:

One set of problem-solving groups had been given the instruction "Do not propose solutions until the problem has been discussed as thoroughly as possible without suggesting any."

The other set of problem-solving groups had been given no instructions. And those people had done the natural thing, and reacted to the presence of a problem by proposing solutions. And people had gotten attached to those solutions, and started fighting about them, and arguing about the relative importance of freedom versus efficiency and so on.

and

Starting out by looking for solutions was taking things entirely out of order. Like starting a meal with dessert, only bad.

While Less Wrong discussants are usually prone to less fighting and arguing than the norm, they are not prone to being inefficient.

What we should have done was forbade any and all solutions until two days after the chapter was released. We had five full days to guess, we didn't need to have all our solutions down the first twenty-four hours. Not to mention that instead of simpler solutions, we continued to look for answers more complex than the ones already proposed after we thought we already cleared the low-hanging fruit.

While some people have made an attempt to analyze first, listing everything in the room, things that only Harry knows, et cetera, the majority of us just proposed solutions right away. This was probably not what Mr. Yudkowsky wanted.

Word of God:

One thing I did notice was that many readers (a) neglected simple solutions in favor of complex ones, (b) neglected obvious solutions in favor of nonobvious ones, and (c) suggested that the correct hints had been put there for deliberately deceptive purposes.

...which in my mind I parsed as keep it simple, stupid, and you all were looking in the wrong direction and why the hell are you all proposing one preposterous idea after another, are you trying to look intelligent or something.

My only conclusion after reading that was that if we drew a map first we probably would of found the more probable solutions a lot quicker. Also reading through 1.5k+ comments full of solutions was headache-inducing.