Editor's Note: Contrary to a previous version of this article, Alan Mulally does have previous turnaround experience.  The Fool regrets the error.

On Tuesday, former Chrysler CEO Lee Iacocca issued a statement that the sitting auto CEOs "are the only ones with the experience and the in-depth knowledge and understanding of how the car business really works. They're by far the best shot we have for success."

I disagree in one case. One of the Big Three's CEOs has in-depth knowledge and understanding of how the car business doesn't work.

Special Forces soldier, or G.I.?
I don't have a vendetta against Rick Wagoner; I'm certain he's a nice fellow and a capable manager under ordinary circumstances. However, he should step down from his position running General Motors (NYSE:GM). Quite simply, he doesn't have a proven track record in turnaround management.

Auto manufacturers are engaged in nothing less than a life-or-death struggle – that requires the skills and experience of a legitimate turnaround artist, not a "business-as-usual" CEO. The difference in attitude and resolve is the same as that which exists between an elite Special Forces soldier and a G.I.

Move over and let these guys drive
Wagoner joined GM straight out of business school in 1977. I'm not saying there is absolutely no way he can pull the turnaround off; however, there is no tangible evidence that he is up to the task. In that context, continuing to bet on him is an unacceptable risk.

Who would I bet on instead?

  • Carlos Ghosn, CEO of French auto maker Renault, and CEO of Nissan, would be ideal. Nicknamed the Icebreaker, Ghosn did a stellar job turning Nissan around. In an interview with BusinessWeek last month, Ghosn was asked whether he could envision a combination with Ford or Chrysler. His reply: "Everything is lined up to push toward consolidation of the industry". However, he "[doesn't] think anyone is going to move" until normal financing conditions return to the market.
  • Wendelin Wiedeking, CEO, Porsche. At the head of Porsche, Wiedeking resurrected the iconic sports-car manufacturer in the 1990s. Porsche is now on the verge of taking a controlling stake in Volkswagen, the world's third-largest automaker. Porsche already owns a 42.6% stake with options on a further 31.5% interest.
  • Marco Tronchetti Provera, Chairman, Pirelli. Tronchetti restructured the tire maker to focus on premium lines. Pushed into optical components and sold the activity to Corning (NYSE:GLW) for $3.6 billion at the top of the tech market in 2000. A possible downside: it would be tough to lure this Milanese sophisticate to Motown. Tronchetti is more comfortable attending the opera at La Scala than rooting for the Tigers.

Thinking "outside the car"
By the way, the GM board shouldn't be afraid to look outside the auto sector, either. In this situation, industry experience can be just as much of a burden as an asset. It's hard to imagine new ways of doing business when all your training has created ingrained models of "the way things are done". In a crisis, bold, unconventional thinking is required. Here are some candidates who don't carry that mental burden of broken models and practices:

  • Jamie Dimon, CEO, JPMorgan Chase (NYSE:JPM). Unfortunately, the probability of Dimon accepting the job is basically null. He already has a great job, and the banking sector presents him with no shortage of interesting challenges right now. Perhaps an appeal to an act of public service would do the trick?
  • Ed Breen, CEO, Tyco (NYSE:TYC). One month after joining Tyco, Breen fired its board and most of its senior managers. As COO of Motorola, he suggested cutting headcount by half, shortly before being headhunted to join Tyco in 2002. Before that, he was CEO of General Instruments, which he sold to Motorola for $11 billion.
  • Mark Hurd, CEO, Hewlett-Packard (NYSE:HPQ), and former CEO, NCR. Hurd is a skilled operator with a laser focus on profitability. Since joining HP as CEO in 2005, he's wrung costs out of a bloated corporate structure, turned HP's PC division around and developed the firm's software business. In three years, Hurd wiped away the Fiorina-era malaise and brought HP to the pinnacle of the industry once more.

What about and Alan Mulally (Ford) and Bob Nardelli (Chrysler)?
Why is Wagoner the only one of the Big Three CEOs I'm calling out? Mulally has legitimate turnaround experience gained at Boeing (NYSE:BA), and he's taken decisive action since joining Ford (NYSE:F) as CEO in September 2006.

As far as Chrysler CEO Robert Nardelli is concerned, I prefer to give him the benefit of the doubt right now, because he has to answer to his private-equity masters. As a portfolio company of Cerberus Capital Management, Chrysler has much tighter corporate governance than its two publicly traded peers, even if we were to add an auto czar to the stew.

Besides, the endgame for Chrysler may not be that far away. The smallest of the Big Three may well be acquired by General Motors.

Weighing the risks of a leadership change
Some of you may disagree with me that Wagoner must go. But what gives you any confidence that he has the expertise and grit to formulate and execute a plan to turn his ward from a value trap into a value creator?

While Iacocca thinks "[changing] coaches in the middle of the game" is too risky, I think this is a case in which failing to switch is by far the greater risk.

Take a drive with further Foolishness:

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Fool contributor Alex Dumortier, CFA has no beneficial interest in any of the companies mentioned in this article. JPMorgan Chase is a Motley Fool Income Investor recommendation. Tyco International is a Motley Fool Inside Value selection. The Motley Fool's disclosure policy goes from 0 to 60 in 12 words flat.