I agree with the point of your question, but I do know that in some cases it's a matter of codebase count. Which is to ask would it be better to have 1 codebase that serves as your website and native views? Or is it better to have X number of codebases for your views based on the number of platforms you'd like to be on? Especially when in all cases the views should be the same regardless of platform/native.
Sometimes native is forgone to provide more centralization of views. It's not always good to custom build for every platform when you want consistency in your UX across all platforms.
I see where you are coming from. And I agree that it's a trade-off.
But I think my point is, that from a usability point of view you simply have no other choice than having X codebases, one for each platform you want to be on, if you are not willing to compromise on usability. I don't know of anyone who tried themselves at the magical "write once, run anywhere" and delivered a consistently great user experience.
Of course, it would be hyperbolic to say that the Khan Academy app has some huge usability flaws. It hasn't. But I'm mostly thinking about another example here: Facebook. They're a billion dollar web company and even they managed to majorly fuck their mobile apps up in terms of responsibility and general snappiness. They tried "write once, run anywhere" and failed.
I'm the iOS developer on the Khan app, and not having to maintain a codebase for multiple platforms is one of the main reasons why we went with jQuery Mobile.
Khan Academy has a lot of custom logic (badges being awarded, points being accrued, and so on) and duplicating that across platforms would be a nightmare.
Sometimes native is forgone to provide more centralization of views. It's not always good to custom build for every platform when you want consistency in your UX across all platforms.
It all depends.
EDIT: Grammar.