父 and 交 are only graphically similar, you would have to make up an story in order to match those characters, but that match is not as beneficial as knowing that 交 are "crossing legs" and 父 doesn't have anything to do with it.
But that's the thing: when you're reading Japanese text, the graphic is all you have. There's no reason why you couldn't see 父 as a pair of crossed legs as well.
Matching characters is beneficial because it reduces learning effort; and knowing that the combined character (交) is unrelated to its components (父 and 亠) speaks for itself, because this is almost always the case. 熊 has nothing to do with 能 or 火. 暗 has nothing to do with 日 or 音, and so on and so forth. You're almost always going to end up with a weird, far-fetched, arbitrary mnemonic.
Even if the book doesn't connect the stories though, should it not at least point out the visual similarity between the modern characters ("watch out: 父 also looks like crossed legs but is missing the person's head") so that students don't risk mixing them up?
I don't know where it reduces efficiency, since making a story up to match does characters just take you more time and effort.
The point is not to have students make up their own stories, but to provide stories that make learning as easy and efficient as possible. And it's more efficient to learn a character as a combination of other characters than to learn it from scratch, regardless of whether that combination is "canon" or not.
Knowing the etymologies (I'm not telling you to learn the ancient form, the glyphs are there to have a quick reference) helps you making the associations between characters natural in a way that at the end of the day everything makes sense.
Are they truly better for making the association though? Do they really still make sense at this point in time? I took a look at some of the other examples:
右: "the right hand is the one that's used for grabbing food." That's nice, were it not that the hand has moved to the left in the meantime. What students need is a way to tell 右 and 左 apart based on the item that the hand is grabbing, not on the hand itself. For example: katakana ロ for Right and エ for lEft.
百: "words coming out of the protruding tongue (白), counting to a hundred." Wait, doesn't 白 mean "white" these days? And who counts with their tongue sticking out anyway?
Better mnemonic: turn the character 90° counterclockwise and you get "|-口口", which bears a striking resemblance to the number it represents.
九 doesn't look anything like an outstretched arm anymore. What it does look like is 力. And you know what the scouter says about his power level, right? Indeed, it's over nine thousand.
Then there are cases where the original mnemonics overlap. 天 and 頁 have the same one: a person with an enlarged head. And yet, one receives the roundabout "that means this person is aware of the heavens" treatment while the other does not.
The book is designed in a way that goes to the pace of learning Japanese language as well. 校 (school) is a kanji that you are going to use very early on. But if you learn 絞 (wringing) early on, it is very possible you end up forgetting it, because in the early stages of learning Japanese language you are not going to find or use that kaji very much if at all. It's better to learn those less frequent characters once you have already learnt the chore of the kanji so know you can enjoy reading more Japanese texts. At that point you'll already know the component 交, so learning 絞 later on shouldn't be a problem, while learning these unfrequent characters early I think its yet unnecessary.
For students who do read Japanese text while they're studying kanji (which is indeed the best way to make them stick), this is fair enough. However, when similar-looking characters are not introduced together, it's all the more important to point them out. Looking at e.g. 九 vs 丸, this book doesn't appear to do that, which results in situations like:
"Wait, 士? Wasn't that 'earth'? I could swear I've seen it before... (Leaf through pages) Oooh, that was 土 which looks almost exactly the same. Couldn't they have told me?"
You are wrong with your first statement since how characters look today is completely related on how characters looked originally. The case of 天 is exceptional since it is an standalone character very rarely used as a component. In these exceptional cases I just give another mnemonic option, but in the majority of phono-semantic compounds the etymologies are plain straightforward once you know them. You can't throw an entire system using just one example.
That's fair enough - I know nothing about kanji etymology, so all my comments are based on what I saw in the sample pages. And what I saw there is that 天 is definitely not the only character that has evolved beyond recognition (see list above), and that the mnemonics for compound characters are just as arbitrary as the ones I made myself when I was learning.
境:
TRKW: "The land limit from which convicted people are sent to in exile"
Mine: "If you stand over there, you can see all the way to the border of the land. Sample word 環境 (かんきょう): That sounds cool! Can (かん) we go there today (今日)?"
Unfortunately the book is not published yet (that's why I run the campaign) so I don't have the kind of testers you've mention, you could be the first one haha!
Alas, I've already learned my jouyou kanji, so I wouldn't be able to give feedback from the perspective of a true newbie.
I'll be interested in seeing what other people say when they try out the book though, especially if they also compare it to other resources.