In what ways might self-ordering mechanisms fail?

Because the net is so young, it is probably much too soon to judge, one way or the other.
But it is worth considering some of the areas in which an private-sector solutions seem most unlikely to succeed:

• Taxation -- By definition, raising the revenue to run "real world" governments will remain primarily the subject of government regulation. Perhaps private sector initiatives could be used to collect some uniform sales tax, thereby reducing counterproductive clashes among local jurisdictions. But it seems likely that the collected "Caesars" will determine how much must be rendered unto them.
• Antitrust -- Self-ordering works best when stability emerging in "lower levels of the protocol stack" (e.g., the market for operating systems) allows new forms of competition at higher layers. But private actors may seek to leverage power from one layer to another. Governments may be inextricably involved in seeking to prevent such excess "rigidification" of markets.
• Contract Enforcement -- Online sites and end users have lots of "self-help" methods for enforcing deals. But in those cases in which physical force is needed to compel one party to honor a bargain, only governments, which have a legitimate monopoly on the use of such force, can be invoked.
• Terrorism and War -- These are, almost by definition, a legitimate continuing concern of traditional governments.
• Redistribution of Wealth and Social Equality of Opportunity and Education -- Hard to see how the self-ordering mechanisms of the net will accomplish these social goals.