Despite the criticism, Hsieh isn't backing down from his decision to continue the "self-management" system known as holacracy, in which employees don't report to a direct manager and are empowered to have more input in decision making.

The criticism only got worse when, in 2015, Hsieh felt the management transition was going too slowly and asked the staff to get on board or take a severance package. Ultimately, 18 percent of his employees chose to leave. Media outlets derided the " radical management experiment " as overly complicated and confusing , and to Hsieh's chagrin, they did not focus on the fact that 82 percent of Zappos' workers remained.

When Zappos CEO Tony Hsieh made the announcement in late 2013 that his online shoe retailer would be getting rid of traditional manager roles, he wasn't anticipating the media firestorm that would follow.

"In terms of what we would have done differently, I think that there's never a good time to make a transition and we probably hesitated too long," Hsieh told CNBC. "So if I could do anything differently, I would actually do it earlier."

Hsieh didn't have to offer the option of a severance package to employees, but he said it aligned with Zappos' policy of treating employees with respect. It mirrors the company's unusual policy of offering new hires one month's salary to quit if they don't love the job (a practice Amazon, which bought Zappos for $1.2 billion in 2009, has since adopted).

Zappos is known for its commitment to company culture — one of its core values is to "create fun and a little weirdness" — and Hsieh hoped the move to self-management would help the company maintain a start-up feel even as it grew.

Holacracy was created and trademarked by software developer Brian Robertson, who grew disillusioned by the traditional hierarchy of top-down management before launching his management-consultancy firm HolacracyOne. With Robertson's lead, Zappos has transitioned from bosses and direct reports to "lead links" who oversee "circles," or certain projects that require certain "roles" being filled. Employees, acting more like entrepreneurs, are encouraged to find multiple roles.

As described in organizational researcher Frederic Laloux's book "Redefining Organizations" (which Hsieh instructed all employees to read), a small turn of a big cog at the top of a traditional management hierarchy can send many small cogs spinning. Try as it might, the reverse isn't true for the small cog.

Under holacracy, however, titles are stripped away, allowing a once lower-level employee to have great impact, Hsieh said.

"As companies get bigger, you become slower moving; there's more bureaucracy. And I don't think any manager is purposely thinking, 'How can I become more bureaucratic?'" Hsieh said.

He speculates that such a reduction in productivity might help explain why so many companies named on the first Fortune 500 list in 1955 aren't on the list today. "If you look at the original list, 88 percent of those companies are no longer on that list. So the default future for companies is death," Hsieh said.

Invoking Harvard professor Edward Glaeser's book "Triumph of the City," Hsieh also points out that cities generally become 15 percent more productive when populations double, while the same cannot be said for companies.