Dick Costolo — who is stepping down as CEO of Twitter in July — has, at a couple of recent conferences, described Twitter CFO Anthony Noto as more than an “accountant” and said that Noto was not brought into the company “just be a CFO.”

Yesterday, the Wall Street Journal even suggested that Noto has emerged as a front-runner to replace Costolo, describing Noto – a former tech banker at Goldman Sachs and a former CFO of the National Football League – as a “take-charge” executive, based on interviews with his supporters at the company.

But promoting Noto to the top spot may not be such a great idea — not based on the experience of longtime executive recruiter Jon Holman, who says CFOs tend to make lousy CEOs. In fact, of the hundreds of C-level executives that Holman has placed over the last 30-plus years, he says he has “never” placed a CFO as a CEO – “nor would I recommend it to someone.”

Holman “doesn’t know Noto at all,” he is quick to say. He adds that Noto could become the “second or third guy in history who has gone from CFO to CEO and been successful.” But he’s highly skeptical of the model for a variety of reasons.

First, it’s likely that until April — when Noto was also put in charge of Twitter’s floundering marketing department — Noto has never managed anything near the roughly 4,000 employees that Twitter has around the world.

“At Goldman, Noto was an analyst, meaning he was a domain expert who knows a huge amount about various industries,” observes Holman. “But he was never managing large numbers of people,  and the people he was managing [in the several years that Noto spent as co-head of the investment bank’s technology, media and telecommunications group] were analysts – not people in marketing, sales, finance, engineering . . .” notes Holman.

More, says Holman, while CFOs generally sound like they know everything, they do not. “Because CFOs sit in on board meetings along with the CEO, they speak as if they understand the business.They understand the financials of the business. They know that, ‘We’re spending 33 percent of revenue on sales and marketing.’ But they’ve never run a sales organization, and their job has never been on the line if there’s a revenue shortfall,” he notes.

Not last, CFOs tend to reign in spending and to generally take the most conservative path possible, notes Holman. That’s probably not ideal at Twitter, which has shied away from making dramatic changes to its platform — and been soundly criticized for it. “Most CEOs are outer directed, while CFOs are inner directed,” says Holman. Using a baseball analogy, he observes that “Most CEO types want to swing for the fences; CFOs want players to hit singles.”

That’s not to say Twitter should rule out Noto completely, suggests Holman. In fact, he could make sense as CEO in the very short term.

Among other reasons why a company like Twitter might bring in a CFO is if “you have investors who think the sky is falling, or, in this case, that it’s a big problem that Twitter isn’t converting tweets to revenue. CFOs generally speak in appropriate adult-like tones and can [massage] investors and assure them that a company will get it all figured out.”

Another argument for promoting the CFO is when a company is just going to sell itself anyway, says Holman. In that case, “What you need is someone who understands how to sell a company, someone who will run a [sales] process, which Noto clearly knows how to do.”

A third reason a CFO like Noto could make sense right now is “if there’s a perception that what a company needs to do is big-time pruning: laying people off, getting expenses under control, those kinds of things that CFOs tend to be really good at.”

Of course, all of these scenarios would be a prelude to bringing in someone else, and Twitter already has an interim CEO lined up in co-founder Jack Dorsey.  Could we see the equivalent of two interim CEOs at the company?

Twitter “can do whatever it wants,” says Holman. “Is it a clever strategy? Probably not.”