Where was this criticism when Bush was in office?
Name a major political story broken by a White House correspondent. A thorough debunking of the Bush case for Iraqi WMD? McClatchy Newspapers' State Department and national security correspondents. Bush's abuse of signing statements? The Boston Globe's legal affairs correspondent. Even Watergate came off The Washington Post's Metro desk.
Here are some stories that reporters working the White House beat have produced in the past few months: Pocket squares are back! The president is popular in Europe. Vegetable garden! Joe Biden occasionally says things he probably regrets. Puppy!
Cox's argument falls apart pretty quickly as soon as you consider the administration using press briefings to release new information (which Cox naturally omits from her article). Look, the White House Press is basically a PR opportunity for the White House. That doesn't make it un-newsworthy.
The right argument to make would be to start discouraging fluff articles, and focusing on substance. To expect the press to use conferences to ask hard questions of the administration.
Instead Ana Marie Cox simply argues, in essence, against press access.