Governments only create shields for organised criminals, everything else is ancient tradition dating back to Hammurabi at least.
Property rights didn't require centralised registries before (and even now court registries are still pretty decentralised), and don't need one now, so what is there left that is a natural monopoly? Nothing.
It was even warned against in the Old Testament:
1 Samuel 8:10-20
10 Samuel told all the words of the Lord to the people who were asking him for a king. 11 He said, “This is what the king who will reign over you will claim as his rights: He will take your sons and make them serve with his chariots and horses, and they will run in front of his chariots. 12 Some he will assign to be commanders of thousands and commanders of fifties, and others to plow his ground and reap his harvest, and still others to make weapons of war and equipment for his chariots. 13 He will take your daughters to be perfumers and cooks and bakers. 14 He will take the best of your fields and vineyards and olive groves and give them to his attendants. 15 He will take a tenth of your grain and of your vintage and give it to his officials and attendants. 16 Your male and female servants and the best of your cattle[c] and donkeys he will take for his own use. 17 He will take a tenth of your flocks, and you yourselves will become his slaves. 18 When that day comes, you will cry out for relief from the king you have chosen, but the Lord will not answer you in that day.”
19 But the people refused to listen to Samuel. “No!” they said. “We want a king over us. 20 Then we will be like all the other nations, with a king to lead us and to go out before us and fight our battles.”
Government
1 Samuel 8:10-20