"General" and "private"? That's two levels, not flat. But ok, so we're obviously using our terms differently. There is still a radical difference between an organization with fixed hierarchical roles and one in which individuals allocate their own time and respect only such authority as emerges during the work itself.
There's another point. In my experience with emergent authority on teams, even if Alice emerges as group leader, that hardly gives her "executive authority". If she begins to insist on making arbitrary decisions, she will soon be knocked down a peg and carry less respect. In other words, these forms of authority (emergent vs. executive) are not the same.
They're somewhat separate, but there is substantial emphasis in current management research on trying to blur them. The worry is that classic executive authority looks increasingly heavy-handed, but the executives still want control. So the goal is to design a workplace such that they get what they want while appearing not to be in hierarchical control. That's a bit difficult since it involves solving a "reverse emergence" problem: how do I set up my workplace so that the emergent authority will tend to emerge in the ways that I want it to? This can involve all sorts of subtle and less-subtle levers: hiring practices, office layouts, perks, "gamification", performance reviews, promotions, etc.
There's another point. In my experience with emergent authority on teams, even if Alice emerges as group leader, that hardly gives her "executive authority". If she begins to insist on making arbitrary decisions, she will soon be knocked down a peg and carry less respect. In other words, these forms of authority (emergent vs. executive) are not the same.