Today's writers, with few exceptions, do not get paid by the word because verbosity is to be avoided not compensated. Accordingly, today's readers prefer brevity -- call it the USA Today approach to literature. Perhaps it's a chronic muscle problem we all have. No one wants to turn a page to finish an article in a newspaper or magazine.
This tendency towards brevity can also be found in the "In Depth" segments on broadcast news programs, which are all of three minutes.
Or notice the decreasing lengths of television advertising - some segments are only about ten seconds long - and fast-paced editing allows three or four scenes in that period. It's simply a global tendency towards ADD. As a species that is the way we are evolving in post-modern society. We no longer take the time to watch the wheat grow.
And yet....some redundancies, such as the "reason why" persist. Write "the reason is" or "here's why" but please do not use them together. It's unnecessary. Possibly the "reason why" is said and written, even by the NY Times, as a crude means of emphasis. I don't know. Whatever the reason, you should take a stand and refuse to participate. Cut out some of these redundancies in your writing and people will absorb what you writer easier.
In my writing seminars I ask students to take an exercise in which they reduce what they have written, or the person seated next to them, or another author by half. It's the "get-to-the-point" exercise that lets you see redundancies in a new lights. You can try this exercise easily on an section of Shakespeare's work. You know how difficult it is for today's modern person to get through Shakespeare. Modern film versions of the bard's works, such as Romeo and Juliet starting Leonardo DiCaprio, use rock music, heightened violence and outlandish costumes so alleviate boredom.
A first step to editing your work, whether it's an email, report, or short story, is to start cutting out unnecessary words and redundant phrases. Once you get into the habit of doing this your writing will improve.