What is "individual sovereignty"?
Rights are granted not by God, not by some internal edict. They come from the society you inhabit.
The world of sovereign individuals is wonderful in objectivist fantasies. In reality, it results in anarchy, for a brief moment before one strongman clubs another over the head, and two other people decide to team up against their neighbors.
Even casting aside the concept of civilization as we know it, you cannot reproduce in a vacuum, nor live in one. You are beholden to others for your existence, and you repay this debt by helping to ensure the continuation of the species. A morality that prizes collective rights over the rights of the individual is fundamental to our biology. Sovereignty, therefore is not a function of individuals.
Lest I be decried as an opposite but equal ideologue, I do see a necessary role for the individualists. The forces of society and government are powerful, and must be resisted: what is bad for one individual is just as likely to be bad for the whole of society. Neither side should ever presume an absolute right: in this battle there is no victory.
You also err in your definition of government. You were nearly correct: government is a natural monopoly on the use of force. The 'competitive market' for government is commonly called warfare. Government is a necessary evil as long as men are capable of violence.