For some people, there is a certain glow to democratic decision-making. And once obtained, there can be no objection to explicit universal consent. But democratic decision-making, and getting explicit universal consent can be very costly.
For example, the high level of democracy for decision-making by the tenure-track faculty at the University of Michigan is one case in point in my own life. This required a lot of time in faculty meetings. Fewer decisions are explicitly democratic at in the Economics Department at the University of Colorado Boulder where I am now, but the quality and degree of consensus in decision-making is nevertheless high here.
Dividing up goods held in common into private property for individuals is a way to dramatically reduce the amount of costly democratic, or more generally political, decision-making that is required. In section 29 of his 2d Treatise on Government: “Of Civil Government” (Chapter V "Of Property"), John Locke points to this as an advantage of the kind of "labor theory of property" he thinks appropriate to the state of nature:
By making an explicit consent of every commoner necessary to any one’s appropriating to himself any part of what is given in common, children or servants could not cut the meat, which their father or master had provided for them in common, without assigning to every one his peculiar part. Though the water running in the fountain be every one’s, yet who can doubt but that in the pitcher is his only who drew it out? His labour hath taken it out of the hands of nature, where it was common, and belonged equally to all her children, and hath thereby appropriated it to himself.
One doesn't have to accept John Locke's labor theory of property in order to see a benefit of some method of dividing things not yet divided up and making them private property.
When I say this, I am thinking of goods that are rivalrous in consumption. The argument for making private property of goods that are nonrivalrous—that everyone could simultaneously enjoy—is much weaker. There the rule that everyone gets to benefit from the good is a very attractive one; society should be slow, careful and limited in ever making nonrivalrous goods private property.