Citi never sleeps, according to Citigroup’s advertising slogan. But for all us taxpayers who bailed out the lumbering banking giant, it probably would be best if Citigroup just went to sleep and never woke up.

“It’s 2 Years In the Red As Citi Logs A Large Loss,” blared the headline in Wednesday’s Wall Street Journal in response to the company’s latest dismal quarterly performance report.

“Pandit Is Running Out of Time to Clean Up Citigroup,” declared a story in The New York Times, noting that Citi Chairman Vikram S. Pandit may lose his job if he doesn’t turn the company around.

Here’s something to consider: Mr. Pandit — or anyone else, for that matter — may not be able to fix Citigroup.

Anyone who’s worked for Citi over the past decade or so will tell you the company is more dysfunctional than your average big company loony bin. And even if the company’s workplace environment is of no concern to Wall Street, investors can’t be too happy with Citi either. From about $50 a share at the start of 2007, Citi stock has fallen to under $4.

The company is an incoherent mess and will find it difficult to attract the right people or change its tarnished image. In our hearts, we all know where it’s headed, so why prolong the agony. Sell off the thing now for whatever value remains in its parts.

If you think about it, the whole concept behind today’s Citigroup is a conceit. Sanford Weill, who made millions by buying brokerage firms and trimming the redundant fat, decided that he would force the government’s regulatory hand in 1998 by having his Travelers Group acquire Citicorp to create Citigroup. The acquisition clearly violated the Glass-Steagall Act, which forbade commercial banks and investment banks from living together under one umbrella. But Glass-Steagall was so 1930′s; it was time for “modern” regulation to meet today’s needs.

We all know where the resulting Gramm-Leach-Bliley Act of 1999 (or, as it should more honestly be known, “The Payoff to the Financial Lobby Act”) got us. The dissolution of Glass-Steagall has spawned banks that are too big to fail, or so the theory goes.

While not quite a zombie yet, Citi is certainly in intensive care. Even in its heyday, the giant always seemed to offer promise more than actual results. Today, its sprawl makes management difficult. Where Weill envisioned himself a Caesar leading Rome, Pandit struggles with a balkanized mess that’s more reminiscent of the Holy Roman Empire.

What is Citi really good at? In which areas does it have a competitive edge? The bank has a big retail banking franchise, but consumer lending is in the dumps and likely will be for quite some time. In other areas, the bank is a mediocre performer.

With the return of the banking system as a whole to a modicum of health, this might be the time to cull the weakest of the herd and let Citi go. Depositors would be protected through the FDIC. Taxpayers no doubt would get the short end of the deal (don’t we always?), but as a 34% stakeholder, the government should be able to engineer something that squeezes a few drops of lemonade out of this lemon.

Rather than risk throwing more good public money after bad, let’s cut our losses. The government should engineer an auction or some other equitable way of selling Citi’s assets to the highest bidder, and then call it a day.

Simplistic? Probably. But it’s time to let Citi sleep.