The following is speculative, and I welcome comments, constructive or otherwise from folks who know better. I am not a journalist. This is not a newspaper article, but a personal blog. If it were a newspaper article, there would be reporting, and fact checking and editing and stuff. Anyway:
The Cod suspects that the place to begin with understanding the decision to allow the Times-Picayune to function as a dessicated shell begins with the logo at left. Chances are good you recognize it. Chances are also good that it's true when you say it's been quite some time since you've looked at the magazine that is the flagship of the Playboy empire. The publication, Playboy, is a relic. (I'm commited to not doing research here, but I doubt that this is a Taste Of Home type thing, where the lowbrow pub no one has heard of is actually vastly more popular than more highly regarded names people talk about.)
So, nobody reads Playboy, but the brand is still strong for selling keychains and airfresheners and as a tentpole for Playboy.com.
A similar thing happened to the Times-Pic's corporate stablemate, Gourmet. Like Playboy, Gourmet was a tony magazine that lost traction in the Internet age, and for similar reasons. (Grab your whisk and double-click, not to put too fine a point on it.) The magazine was losing money on Reichl's watch, and Conde management elected to suspend publication of the print mag, rather than sell it. By doing so, they kept the Gourmet brand, killed the magazine, and kept the name for a blog.
For Playboy and Gourmet, the brands are profitable, even though the eponymous publications are not. There are, quite probably, folks who would take the crack at running the Times-Pic as an actual newspaper, one that comes out seven days a week, and in a way that poor folks can read. Lots of them don't have broadband. However, same boss, similar math, in that one imagines that the Times-Picayune/NOLA.com, functioning as a news flavored media brand, rather than as a newspaper, might be profitable for the Newhouses.
These are a series of semi-educated guesses, but my guess is that this is not the last media brand vampirism we will see.