Although, I believe that one could divide your points into two fields: General and Specific.
I do agree with you on the general stuff. So I will not dwelve too much on that. They (can't) doesn't need to be perfect, and their vision of the events is limited unlike us veiwers.
E.g this is why vigilantes will never work on real life. WE as an audience knows everything we need to draw a conclusion that (e.g) 'Batman' is a good guy, but the people in that universe don't.
However, I'm afraid you tried to apply general truth to a very specific story in which I believe this can't be applied.
But instead of going right into it, since I do actually believe that I somewhat talked about it; I want to try to convey you how I feel about this person. And then walk through why I believe "your" general points doesn't really apply here.
Imagine you're watching a House episode. Maybe you haven't seen him, but you know the show is about dr. House solving "mysterious" diseases.
A woman walks in, her stomach is swelling, she has morning sickness and she craves the most unusal food combinations.
House can't for the life of him figure out what is wrong with her.
Now he get the information that she has a boyfriend and they have been doing it without protection for the last months.
Nope, House is still stumped...
But do YOU know what is happening to her?
Spoiler, she is pregnant.
I get that "geniuses" sometimes skip necerssary steps, and that they've flaws like everyone else.
But these flaws often come up in something else then their expertise. House is a grumpy a-hole with a drug addiction.
And some steps are so fundemental that and incoperated into the job that NOT knowing them IS a sin. Since they are missing knowledge that is essential to even do what they do in the first place.
Let countinue with the hospital trend as an example:
Not coming to the conclusion that the women get pregnant as a doctor, that is a sin, Dr Cox (from Scrubs) not knowing that a patient had "rabies" (I think) before it was too late and did a huge (but possible) mistake... Well, if I remember my own example right, "rabies" is apparently rare in the US...
And I would say that not knowing about the concept of "running away" as a detective is MORE sinful than a doctor not knowing about pregnancy.
Since running away is a human respond. It's a huge part of human psychology. And if you as a detective can't even nudge on that possibility, you fail big time. Not just this time, but most likely everytime.
But what about his perspective. His knowledge on all this.
I'd already mentioned two examples to counter this respond. But you weren't happy with them and brought up your own "what ifs".
Sure, I can give you those.
How about the fact that:
1) He knew she was beaten and abused.
2) He knows the parents are lying about her not being home after school.
He even ponders on these two fact (and still doesn't even nudge on the possibility of a runaway)...
And let me ask you this again: WHAT do point out she has been kidnapped in the first place?
We (he) has had five insights:
1) Beaten
2) Lying parents about her being home.
3) Teacher "confession"
You think he might be lying which is possible, but the whole situation in itself (from the detective's perspective) reaks of strangeness.
4) Old lady's testomony.
You made a fair point, I will give you that.
5) He knows she is with someone (right now).
But once again; why kidnapped?
Lets look at all "general" possibilites for cases like these:
1) Kidnapped -from school
2) Parents killed her
3) Runaway -alone
4) Runaway -suicide
5) Runaway -kind soul taking her in
6) Runaway -kidnapped
So why just kidnapped, why must malice had been involved?
I never said that he could still believe that she was kidnapped. But when WE see him getting these great insight (like parents lying of her not being home), THINKING it's strange, and is still not able to think "outside the box" is just weird.
The ONLY thing I could think of that may led to a conclusion of her not running away is her not having friends (anywhere to go).
But that is rather weak excuse to dissmiss a potential runaway (especially since he haven't even THOUGHT of the possibility yet, which IS my issue).
But what would YOU think after having these 5 insights? Not as a reader knowing, but in general after hearing this.
Would you be hardcore on the path of "kidnapped with malice" without even considering the other possibilites?
Let me tell you this, YOU as far as I'm concerned is a normal human being, and yet I believe YOU should have the intelligence to see past certain things. But for this genius detective I should not?
And your highnote... Sorry, but it was kinda weak... I don't want to go to hard on it since I can be "one of those" as well... But at least remember this is a translation where the small stuff can get lost... Especially semantics.
And sorry to inform you that you most likely will have to follow up.
This is a discussion afterall. But if you don't want to, hey, I don't blame you.
Ps. I understand why you put "spoilers" on something that didn't spoil...