I've only experience with Remembering the Kana, but it worked, and worked very well, for me -- not because I immediately knew them by intrinsic sight, but because of the silly stories with each one would quickly bring them back into memory.
If you're talking about learning Kana, then my argument would be that some flashcards or computer based drills are going to be a more efficient method of learning, if perhaps less pleasant, than reading a story for each character. And why go through this circuitous thought process of seeing the character, recalling the appropriate story, and then divining the meaning? We don't do that for our letters, and we don't do that for simple arithmetic.
About a year (~2000 kanji). That's casual study though, and I restarted once after an idle period.
> How well can you read?
I can recognize and write just about any of the general use characters. But kanji is not vocabulary. Instead, going through RTK has made studying vocabulary tremendously easier. It's given each character a kind of "identity" in my head. I can also guess the meaning of many compounds by the keywords given in the book, but this is just a bonus, real reading comprehension should be attained with vocab study.
I'm not sure if you've actually read the book, but it's no snake oil. It makes no claims to the amount of time or effort you'll need to finish it. It's simply a method to learning kanji that tries to make the most out of your memorization capabilities. It does this by presenting them in a more convenient order (progressively building up the characters), and throwing etymology (to some extent) out of the window in favor of your own personal mnemonic stories.
I would not be surprised if the parent hasn't read the book or tried it. Most of the complaints with his method seem to come from people who have never tried it.
Maybe other people don't or can't learn that way, but these silly picture stories are enough to let me memorize characters I've never seen before so that I can look them up later.
I agree that eventually the stories should be forgotten, but initially, they are significantly better than my normal memory.
In fact I am starting to forget the stories of the kanji that I am exposed to regularly. However, some of the general use characters appear pretty infrequently, and for those the stories are still invaluable. I like Greg's training wheels analogy below.
Another advantage is that the stories provide a check for characters I also know visually. So if I'm writing a character from my visual memory I might be reasonably confident that I'm writing it correctly, but if I can also remember the story then I am sure.
Of course doing RtK doesn't teach you any Japanese, but since I did it I find Japanese vocab acquisition much easier. Maybe it's like learning English when you already know Greek and Latin.
The point is to just get you familiar with the kanji so they don't look like a foreign language anymore. After that, you learn how to read them in sentences and words.
Also another point is that you don't have to "practice, practice, practice." Some characters I can remember after only writing it a few times because I have the story associated with the character. It sure beats the Asian method of writing out each character hundreds or thousands of times.
The Heisig method is just meant to be the first step.