Jeffrey Cohn runs a program that trains and grooms future CEOs — and he said that Uber's board isn't doing the best job of it at the moment.

The ride-hailing start-up has been without a CEO since June, when founder Travis Kalanick stepped down following a wave of bad publicity. Since then, the board has been torn between Kalanick's loyalists, the picks of top shareholders, and the opinions of the company's many other investors and employees.

That's bad business, said Cohn, founder of CEO Fellows, who appeared Friday on CNBC's "Closing Bell."

"This is an easy search — this company's on cruise control to a $100 billion IPO," Cohn said. "And the board just can't get out of the way of each other. It's like a confederacy of dunces here. They're suing each other, they're fighting, it's public bickering. So what CEO worth their salt is going to want to come into a board like that, that's so dysfunctional?"

While Travis Kalanick is a great founder that's elevated Uber, Cohn said he's also a cautionary tale that passion, aggression and vision only go so far in situations like Uber's workplace culture investigation and sexual harassment allegations.

"He's casting a long shadow. So I think it's going to be difficult for them to attract the best talent under these circumstances," Cohn said, adding:"It's that lack of soft skills that can really trip you up. Those take months and years to develop. So the lesson for all these future Travises is to start early and really think about the EQ."

Former GE boss Jeff Immelt has been floated in the press as a contender. While he may be "strange pick" according to Cohn, Immelt's likely up to the challenge.

"You know, he has some gray hair. And I think the most important thing for this company is a little bit of gray hair in the culture," Cohn said. "The job is all about the culture, and he has been in a situation where he's run and set a culture for a large, complex global organization."

Any potential CEO will have to weigh the "once-in-a-generation opportunity" with pressure from investors that's likely to grow if the company goes public, Cohn said.

"I certainly am in favor of everybody getting rich," Cohn said. "But there's a lot of downside. So if you don't think the market cap is worth the $70 billion right now, then that person's got to get it to up to a hundred, or else it's going to be a total disaster for that incoming CEO."