I don't see any reason why more competent people would prefer omission of a key step in a proof with remark "left to readers as an excercise". If you want to save time, you can surely skip it while reading. Why shall the author make the choice for the reader?
Especially in math, even textbooks which are intended to present complete overview of some subject have these excercises to the reader. I like to read books from the beginning to the end, but this is exactly what makes it impossible for me to do with math books. It can be refreshing to stop reading at some moment and have to think about some detail, but to do it repeatedly, knowing that I am losing time trying to figure out something which could be explained on two lines, is frustrating. I read books and papers because I want to get the information as efficiently as possible, not because I want to eventually rediscover it for myself. Not much to do with competence, I believe.
Added: I also find "excercise to the reader" mildly offensive, as the author is saying that it is trivial for him, but not for the readers, who should improve their skills by making the excercise. Such sentences aren't surprising in undergraduate course textbooks, but when the audience are competent people, it seems inappropriate.
No, I don't mean that the news media are biased politically. I mean that authors are biased by the media they use.
I'm learning about support vector machines (SVMs). There are a lot of books and articles written on SVMs. There are also a whole lot of video lectures on SVMs at videolectures.net (see "kernel methods").
People go into much greater detail in lectures than in text. I like to work with text. I'd like to have a text on SVMs that goes into as much detail as videos on SVMs usually do, and works out the ideas behind the concepts as thoroughly, but no such text exists. For some reason, giving a 5-hour lecture series in which you describe the motivations, applications, and work out the mathematical details is acceptable; but writing a text of the same level of detail, which might take only 2 hours to read, is not.
Perhaps this is because writers are motivated to keep pagecounts low. But pagecount no longer matters with electronic articles. Yet writers still don't want to explain things thoroughly. They certainly aren't saving their readers any time by leaving out intermediate steps. A longer article would take less time to read (and possibly less time to write). Another problem with the pagecount theory is that texts routinely include footnotes and appendices, contributing to the pagecount; yet relegate them to the back of the book, as if embarassed of them, despite the fact that this makes them very difficult to use.
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". For some reason it is considered bad form to write out all of the steps in a proof, even if adding one or two lines could save the reader five minutes of puzzling. I read an electronic article yesterday where the author said, "These two equations are actually equivalent. Do you see why?"
I think people have adopted a set of cultural biases about what is appropriate in lectures vs. in writing by simply counting observations, without thinking about the systematic sample bias. Speakers speak the way they've seen other speakers speak, without recollecting that most of those speakers were instructors. Technical writers, meanwhile, are picking up their cues from authors of textbooks, which are written with the assumption that a person will be on hand to take you through the details; and applying them in situations where no such person will be available.