With private provision there may be privacy costs involved in monitoring use of the good. A private supplier would provide too little of the good. A decentralized market economy requires the establishment of property rights. A property right is an exclusive right to use or sell a good within limits. The existence of property rights allows voluntary market transactions to work.
Government establishes and protects property rights more efficiently.
Private protection can result in the free rider problem . A free rider is someone who uses the goods or services provided by others without paying for them. The free rider problem means that too little of the good is provided. It is generally cheaper to have a single agency provide property rights. The protection of property rights probably requires coercion.