You need management, but what you need is a constitutional workplace where there are real protections (e.g. people have the right to choose the team they work on, within reason, and performance reviews are for compensation upgrades only and not part of the transfer packet) that employees get to vote on and that limit management's power. I'd even consider extending that to a profit-sharing model that's more transparent and fairer than startup equity, which is based on some insultingly small percentage of some possibly-huge-but-how-would-you-evaluate-that number in the future.
There are several problems with "no managers". First, many tech companies tell every engineer, down to the junior coming out of college, that he'll be reporting directly to the CTO. Then he gets there and learns that he will actually be evaluated by his tech lead, who answers to a (possibly titled, possibly not) full middle manager... who answers to the CEO. It's dishonest as fuck, but really common in the startup world to use "flatness" to make a position sound closer to the action and to power than it actually is. "Flat" organizations are often alluring lies that hide the real power structures. It doesn't matter if Bob is an idiot who works 15 minutes per week; if the CEO will take Bob's word over yours when it comes to your value to the company, then Bob is your boss.
Second, if there are going to be power relationships anyway (and there are) it's better to answer to a titled manager with a completely different job description, than to someone who's technically same-rank and therefore also competing with you for work. You won't win in that situation.
I'm skeptical because I feel like managers are akin to cops. There are some really shitty cops out there, no question. But you need them, because the alternative is... that a police-like force emerges (organized crime would rather have order than violence) but it's not accountable to the public and the costs are erratic. With public police, you pay taxes and can vote officials out of office if they make bad calls. With emergent private police (thugs) the extortions and bribes can go up from day to day for any reason or no reason at all.
What's wrong in most companies is that the police are making the laws, rather than enforcing them for public benefit. Because most companies don't have any constitutional structure or real protection for workers, the law is "if you have power, you can do it" so middle management ends up making the law up as it goes, in pursuit of its own interests (maintaining and consolidating power). Management is a fine concept if management is put in its place and empowered to enforce but not legislate. I don't know how to put this into practice. It's hard, because you have to fight human nature.
In other words, the problem is the lack of constitutionality in corporate governance. Corporations are pretty much all run as dictatorships. That can work surprisingly well (in terms of efficiency and competitive supremacy) when the dictator has something unique to offer. It ages poorly, because the dictatorial role gets handed over and eventually it's in the wrong hands and everything goes to hell. Imagine what would have happened to Singapore if anyone other than Lee Kuan Yew had been in that position. Dictatorship only works when you have a very rare type of mind and get a true philosopher-king. (It's not about pure intelligence, either. It takes charisma and focus, too.) That doesn't describe most corporations or corporate leaders. For the most part, this dictatorial model leads to low morale, stagnation, and mediocrity.
That's why people hate management: we've all picked up that it's serving its own interests rather than that of the employees or of the company. All of this said, "no management" tends either to produce an emergent and less accountable management/police force or it tends to mean that power is concentrated at the top. So I tend to think that this "no more bosses" movement is somewhat of an overcorrection.
You mention that most companies don't have "constitutional structure," are you talking about an employee bill of rights?
What would you think of the idea of running a company literally like a representative democracy? A constitution and bill of rights, management as elected officials, employee "voter initiatives", projects compete for talent internally etc?
It might not be perfect either, but perhaps a good middle ground between militaristic top-down bureaucracy and Zappos-style anarchy?
The middle ground you described is a brilliant idea. What you probably need to enforce it, at first, is an enlightened dictator (i.e. the 1% who won't get power-hungry and fuck everything up).