Thing is, when the New York Times was "the newspaper of record", everyone read it. When they only print what will pass muster with the howling mob, for fear of losing their jobs if they offend, then only the howling mob will read it. But the howling mob doesn't have enough members to support the New York Times.
That is, catering to the most vocal segment of the Right Thinkers is a ticket to an ever-shrinking readership, because 1) everyone who isn't a card-carrying member of the Right Thinkers leaves, and 2) the Right Thinkers shrinks as the majority repeatedly throws out people for not being right thinking enough.