Is Mackey too wacky to be CEO?

(Fortune) -- Carl Reichardt, the tight-fisted former chairman of Wells Fargo, once received staff proposals for capital spending improvements while sitting in a chair with torn upholstery and the stuffing hanging out. Ex-Marine Hugh McColl, another notorious former banking industry CEO, once pulled the pin of a dummy hand grenade during a meeting in his office to see who would flinch.

The hall of fame for eccentric corporate chieftains has a new entrant, with the news that John Mackey, founder and CEO of natural foods purveyor Whole Foods (Charts, Fortune 500) had, for several years, posted rah-rah comments about his company on a Yahoo (Charts, Fortune 500) message board under a pseudonym.

Whole Foods CEO Mackey.

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Setting aside the legal ramifications for the moment -- so far, the SEC has not taken any formal action -- we're left with a few big questions: What the heck was Mackey thinking? And what, if anything, should his board do about him? Is Mackey, a 53-year-old vegan, simply too wacky to remain CEO? Or, as some of his many admirers believe, is his decidedly non-corporate behavior a large part of his appeal, and the success of Whole Foods?

To get at the first question, we hopped on the couch of corporate shrink Josh Ehrlich, a New York based executive coach with a Ph.D. in psychology. Mackey has said on the company's web site that he posted for "fun," and that he never intended "any of those postings to be identified with me."

At first glance that seems extraordinarily naïve, especially in this day and age, but Ehrlich sees more to it than that. What motivated Mackey, he argues, were the "three P's -- pride, passion, and pressure."

Pride and passion in the company he built from the ground up, and then pressure, both external and internal, to do well -- even if it meant bashing rivals like Wild Oats, whose former CEO, Perry Odak, was a frequent target of Mackey's pseudonymous fusillade.

As for Mackey's apparent disbelief that he was outed, Ehrlich chalks that up to the delusion that online discourse flows freely, with no repercussions. "We think that by doing something online that somehow we are hidden and we can pretend that we are behind this screen," he says.

Indeed, several CEOs -- most notably Boeing's (Charts, Fortune 500) Harry Stonecipher, and, reportedly, Starwood's (Charts, Fortune 500) Stephen Heyer -- have recently been let go for inappropriate emails. But in those cases, the correspondence in question had their names attached.

In Mackey's case, "he could pretend that this would never be seen," Ehrlich says. (Through a spokeswoman, Mackey declined to answer written questions from Fortune.)

Mackey's behavior is also of a type found among entrepreneurial CEOs, usually unconventional individualists, who often "find themselves at odds with the culture and laws of the corporate mainstream," says Advertising Age editor Jonah Bloom. Mackey had earlier launched a caustic, 14,000-word online diatribe at the Federal Trade Commission, which is suing to block Whole Foods' proposed merger with rival Wild Oats. (A two-day hearing to decide whether an injunction will be granted begins July 31, and a Bear Stearns analyst said Thursday he is now more convinced that the FTC could prevail.)

So, faced with an iconoclastic CEO whose odd behavior is, at best, an unneeded distraction, and, at worst, unethical and potentially illegal, what should the Whole Foods board do?

"The CEO needs to anticipate risk, not cause risk," says Betsy Atkins, who sits on the boards of Chico's (Charts), Polycom, and Reynolds American (Charts, Fortune 500). "If one of my CEOs did this, you have to consider his integrity, and question whether he should continue in his role." Governance guru Charles Elson agrees: "It shows a real lack of discretion and wisdom. The board has to do something about this."

But what? A public apology? Termination? "It is time to boot this guy out, but I doubt the board will," says Jeff Sonnenfeld, a CEO and leadership expert at the Yale School of Management.

Instead, maybe the board would consider a demotion out of the corner office to a position where Mackey can't cause as much trouble. "It's time to wheel out one of those wacky titles, perhaps 'chief brand evangelist,'" says Bloom.

There, Mackey could continue to be Mackey -- preaching the natural food gospel, railing against Whole Foods' naysayers, going on 2,500-mile backpacking trips in his spare time -- while not impacting shareholders, who, after all, own the company.