Brian Dunn on September 30, 2009 (LUCAS JACKSON/REUTERS)

Since its founding, the consumer electronics retailer Best Buy has been run by three men: Richard “Dick” Schulze, who founded the company in 1966; Brad Anderson, who oversaw its continued expansion; and Brian Dunn, whose short tenure atop the big-box retailer came to an abrupt end on Tuesday amid an investigation into his “personal conduct” at the retailer.

What may be more remarkable than the fact that the company has only had three CEOs is that each man spent most of his career at the retailer. Schulze co-founded the company, which was originally called Sound of Music. Anderson started out as a sales clerk on the store floor. Dunn also got his start as one of the company’s “blue shirts;” his mother was one of the company’s first employees.

A history of insiders is typically a good thing: It is a sign that succession planning is taken seriously, it elevates people with institutional knowledge and unsurpassed expertise of the organization, and helps to motivate talent within the company. Few things say “you have a future here” to a sales clerk selling TVs for $10 an hour than the company’s last two CEOs getting their start in the exact same spot.

But something tells me the company will be looking at outsiders when it names its next CEO. In the wake of Dunn’s departure, the company has named G. Mike Mikan, the former CFO of UnitedHealth Group and a Best Buy board member, as interim CEO. But the company has also developed a search committee that is expected to look outside its ranks for the first time since its founding.

Executives with digital experience—rather than simply retail skills—are expected to be in the running. The company has been struggling as consumers head to Apple’s sleek stores to buy that company’s must-have gadgets or stop into Best Buy to preview products, but then buy them on Amazon. The company’s new CEO, executive search consultant Les Berglass told The New York Times, “must recognize that as much as they perceive of Walmart and Target as their main competitors, their real competition is Amazon,” he said.

An outsider would also likely be more willing to shake up the company’s plans, which have come under intense pressure from investors. The Wall Street Journal reports that Best Buy’s big-box stores had operating income per square foot of $50.61 in 2006, a number that fell to $18.52 last year, according to Craig Johnson, a retail consultant. (Apple, he says, earned an astonishing $1,100 per square foot.) The company reported a $1.7 billion fiscal fourth-quarter loss, partly due to restructuring charges.

Though Dunn rolled out a restructuring plan two weeks ago, Best Buy shares fell on news of the plan, which was met with skepticism by Wall Street. Still, it’s unclear how much latitude an outsider would have to make further changes: The board reportedly helped to craft the restructuring plan, and the initial announcement about Dunn’s departure said “there were no disagreements between Mr. Dunn and the company on any matter relating to operations, financial controls, policies or procedures.”

An outsider would also be able to start afresh, untainted by the “personal conduct” investigation that is ongoing. Questions could arise about how much insiders knew, how long they knew it, and when the investigation started. A CEO from the outside would be free from any association to the probe.

An over-reliance on outside leaders is never a good idea—it tends to drive up executive pay, can lead to a cult or personality around the supposed white knight, and, especially if they come from other industries, can be a mismatch that hurts the company. But in this case, Best Buy might benefit from an outsider with digital expertise for a changed retail world, a willingness to change course, and a background separate from the current investigation. Sometimes, fresh eyes are the only way to see where the problems—and their solutions—really lie.