Some reasons I could think of, off the top of my head..
* Doing a lecture series only takes as long as it takes to film. There is no post-lecture work, such as rigorous editing or re-organization of ideas.
* You can rant. As long as you are speaking and guiding the listener along with you, you can easily make reference to things that are explained later on or go on tangents. If you are publishing an article and go off topic, people might skip it sections all together or become confused by the switch as they only skim text.
* Publishing a piece of text in your name is a bigger deal than posting a video.
* Lectures let you see how well your audience is getting it (assuming you're lecturing to an audience). So you can tell what's making sense and what's not.
* You can talk faster than you can write. In fact, in my experience, I can talk about as fast as I can think. I can't write as fast as I think. This makes me inclined to skip over some thoughts while I'm writing, simply to keep up.
Incidentally, I don't see why the first point ("There is no post-lecture work, such as rigorous editing or re-organization of ideas") is really an advantage of lectures. Certainly there are many lectures I've seen that could have used some reorganization. And, at any rate, any decent lecturer will do preparation beforehand to organize the presentation.
* It takes time to figure out which details are essential and which are not. When extemporizing about a topic, which happens frequently no matter how well you prepare, you may throw in extra material because you don't have time to figure out exactly which bits are necessary to form a coherent picture for your listeners. Academics especially will err on the side of verbosity: adding a few extra facts feels like a lesser evil than leaving an important point unaddressed.
* When writing a book, you have time to pick the very best and richest examples, accomplishing as much as possible with each detail. In a lecture you may end up using many details, because each detail only illustrates a small part of what you're trying to say.
* Lectures are delivered live, with no opportunity for rereading, so repetition is important. In a book, a difficult point should be stated as clearly and precisely as possible with the expectation that a reader who is confused will reread the point many times until it becomes clear. In a lecture, you can't simply repeat yourself five times because a few of your listeners didn't understand, but you can't abandon those listeners entirely. You have to give them time to grasp the concept while at the same time keeping your other listeners engaged. Going over many examples and explaining the connections to related ideas serves the dual purpose of clarifying your point for those who are floundering and providing extra information for those who understood you the first time.
Not true that "a lecture series only takes as long as it takes to film": they entail lots of preparation, including re-organization of ideas BEFORE the lecture.
I think that live feedback from an audience is more important: In a lecture you can relatively easily gauge audience interest and comprehension of details, so you get rapid feedback about the audience demand for the focus and degree of details.
While not applicable to other areas, I know that conference papers in CS (and many journal articles as well) have stringent page limits. Thus, given a short amount of space, you have to prioritize what goes in the paper.
Secondly, when writing an academic paper, the primary goal is to keep the reader/reviewer interested. That is why proofs, simple calculations, and other such "trivial matters" are relegated to appendices -- the flow of the main paper should not be disrupted by these.
Finally, one advantage to omitting steps is to ensure that the reader is putting in effort to understand the concepts. Fully drawn-out text would invite people to do conceptual "copy-paste," which would cause problems when they try to apply their knowledge to real-world problems. An analogue of this phenomenon is seen on the web with php programmers, who frequently copy-paste php code found from various tutorials without really understanding what's going on.
However, for in-depth tutorials published online, I agree with the author that super-detailed texts are best. And here, the practical issue of the time spent by the author typing, checking, and revising the tutorial starts to become the dominant reason why tutorials aren't so detailed -- at some point, it's simply not worth the author's time.
Verbal communication is just inherently different from communication through the written word.
We've all encountered teachers who lecture "as though they are reading from the textbook". It's the same information, so why should it matter?
I think it has to do with verbal communication being more about interacting with other people. When I see another person lecturing (live or through video), I find it easier to stay focused on what they are telling me. There are all these visual cues that add some extra hooks. And then, of course, the verbal ones. The accents, the pauses, the little jokes or references that are thrown in.
Just think of your favorite stand-up comedian. Compare reading a transcript of your favorite session to an audio recording of that same session to a video of that exact same session. You probably experience them all very differently.
So instead of comparing a text with a lecture, where both share the same subject matter, compare a text of the lecture with a video of the lecture. (Bonus points for comparing a text on paper with a video of some guy reading that paper aloud).
I think lectures are better/detailed due to feedback from the audience. The lecturer can guess when to go fast and when to go slow(and explain more) by gauging the audience. In some cases the author of a book can guess what his audience can think and provide explanations in advance. But thinking what your reader might think is hard. I feel in the case of the author of the article it was just an accident that he is very similar to the audience that was present during the video lecture.
>It's especially bad in math, in which writers have a long tradition of deliberately concealing difficult steps and leaving them "as an exercise to the reader".
You're supposed to do those exercises. If you're a programmer think of them as unit tests. In technical subjects, most of the information is contained in the problem sets. For that reason I'd actually say the texts are more informative - more detailed.
Yeah, it's ok when you know the answer (e.g. when you have to provide a proof of some theorem), but when you have a excercise section at the end of the chapter some books do not provide answers to those excercises. It's like having unit tests without knowing if the correct solution is e.g. 2 or 5.
I'd say I almost always get 70%+ of the benefit just by having an answer. And there's other techniques that help, eg checking one problem against other problems, getting a bound on your error, asking on forums/mailing lists, etc.
* Doing a lecture series only takes as long as it takes to film. There is no post-lecture work, such as rigorous editing or re-organization of ideas.
* You can rant. As long as you are speaking and guiding the listener along with you, you can easily make reference to things that are explained later on or go on tangents. If you are publishing an article and go off topic, people might skip it sections all together or become confused by the switch as they only skim text.
* Publishing a piece of text in your name is a bigger deal than posting a video.