It’s a leadership drama to rival any in business or even Shakespeare. It’s such a mess that the company’s biggest and most pressing need, the naming of a new CEO, has almost been pushed out of the headlines. But as the boardroom drama plays out, there is a major search going on, and a new CEO may be named soon—word is by Labor Day. And the latest in the parlor game of who-will-it-be is that the shortlist is said to be down to four men.

This has riled many who feel quite strongly that Uber’s new CEO needs to be a woman. After all, Uber is first and foremost facing a crisis of culture —a culture that was toxic generally but particularly so for women, as detailed initially in former employee Susan Fowler’s blog post alleging rampant sexism and later through investigations that led to the firing of more than 20 employees over sexual harassment claims. Fixing Uber’s problems begins with fixing the culture—and a female CEO would send a signal that everything about this company is going to change. It would be symbolic and important.

Strike me down if you like, but I don’t think the Uber CEO needs to be a woman, and I’m neither surprised nor aggrieved that the final candidates are all men.

I am all for women CEOs. I am a longtime co-chair of the Fortune Most Powerful Women Summit and I firmly believe the reams of research that show that companies perform better when diversity is reflected (take a look here and here; how could you disagree?). I also believe that women lead differently and have distinct advantages over male leaders in ways that are going to become more and more important. I believe we should and will see more female CEOs, and that the lowly 6.4% figure for female CEOs of Fortune 500 companies—and the number of female directors and other C-suite and senior leaders—must increase and will increase.

But the naming of the new Uber CEO is not going to be the headline moment for that effort that so many want it to be. There was much speculation early on that the new Uber chief would be a woman. Initial names floated included Facebook COO Sheryl Sandberg, Yahoo’s former CEO Marissa Mayer, and CVS Pharmacy president Helena Foulkes (who was reported to be on the short list for the COO spot when that was Uber’s pressing need. Remember those days? Seems almost quaint.)

More recently, Recode’s Kara Swisher reported a long list of top female leaders who were not interested: Sandberg, GM CEO Mary Barra, YouTube boss Susan Wojcicki, and Uber board member Arianna Huffington. Most notably, the Uber board entered into advanced talks with Hewlett Packard Enterprise CEO Meg Whitman, but, said to be fed up with the unprofessionalism of the process, Whitman pulled her name out of consideration abruptly—leaving the all-male shortlist, which is said to include former GE CEO Jeff Immelt and three other male CEOs.

Uber needs to do one thing only. It needs to “solve for X,” “X” being fixing a business, culture, and company that has been almost mortally wounded (in addition to its culture issues, Uber faces a legal challenge over accusations it stole competitive secrets, a federal inquiry over its use of software to evade authorities, steep losses and an increasingly competitive landscape, among other challenges). For the benefit of Uber shareholders, employees, drivers and riders, it needs to be the best person for the job, period. Uber doesn’t need a woman CEO specifically; it needs the best person. And there are many reasons that person is unlikely to be a woman.

Even beyond the leadership and culture crisis—if it’s even possible to look at the company that way—finding the right female CEO for Uber would be a challenge, says Jana Rich, founder of Rich Talent Group and one of Silicon Valley’s top executive recruiters (and who is not involved in the search, which is being handled by Heidrick & Struggles’ Jeff Sanders). “Let’s assume for just one second that everything was going well for this company,” she says. The size, scale, hyper growth rates, and complex nature of the business Uber operates in, Rich points out, poses a very specific set of needs in a leader. “Taking out any of the performance issues, it said to me it’s likely to be a guy because very few women have dealt at that level of scale and complexity and rapid growth,” says Rich. Even though there are women CEOs of the biggest Fortune 500 companies, for example, there are simply far fewer of them with experience transforming large companies than there are men.

A potentially bigger issue: The Uber opportunity is the very definition of the “glass cliff,” the phenomenon in which women are much more likely than men to be named to lead companies that are struggling or in crisis. Once there, the theory goes, women face more pressure than male leaders to perform, and are essentially set up to fail. The reasons cited for this are many: women tend to seek out bigger challenges to distinguish themselves; companies in crisis see naming a woman as an opportunity to gain instant “credit” for being progressive; some have pointed to a belief that women are better-suited to lead stressed companies because they can be more nurturing and intuitive.

The research suggests the phenomenon is real. As Fortune reported last year, one study of more than 50 women CEOs appointed to Fortune 500 companies through 2014 found that twice as many women CEOs were appointed during times of crisis as male CEOs. Examples of this abound, from former Xerox CEO Anne Mulcahy (who notably never fell off of the cliff) to former Lehman Brothers CFO Erin Callan to Sheri McCoy, who recently stepped down from Avon, to British Prime Minister Theresa May. Perhaps most illustrative is the case of Marissa Mayer, the recently departed Yahoo CEO. When she was named to lead the struggling company, the expectation among many was that that she would emerge unscathed—if she failed, it would mean Yahoo was unfixable. But she was unable to fix it, and is still being blamed. Is it any wonder women leaders may be wary of taking that kind of risk? (It should be noted that plenty of men, Swisher and others have reported, including former Disney COO Tom Staggs and former Ford CEO Alan Mulally, have said they don’t want Uber’s CEO job, either).

And there’s no reason the right male CEO couldn’t do what’s needed. As any reader of women leadership literature knows, in order to boost the percentages of female leaders, we need the help of men. A strong leader who can overhaul a toxic culture could be male or female—and Uber’s culture issues go well beyond sexism. (And anyway, male CEOs have righted sexist workplaces before: witness Blake Irving’s success at transforming GoDaddy’s culture.)

I’m not suggesting it’s equivalent, but Uber already has many women in high-ranking positions. And the rest of its C-suite is still a roomy place—in addition to CEO, it is also currently without a COO and CFO, spots that could be filled by women. (Not that that would have anything close to the significance of naming a female CEO.)

Turning Uber around, fixing its culture, and taking it public is a major task. So is lifting the number of women CEOs of big and high-profile companies. The Uber board shouldn’t bend over backwards to try to do both things at once. Especially not by Labor Day.

(For an inside look at the rise of Uber and Travis Kalanick, see Fortune’s Adam Lashinsky’s new book Wild Ride.)