Real libertarians; not the hippies with no understanding of Lysander Spooner, Mises, or Heinlein; have a point about how private (aka polycentric) law beats socialized law. The vastly simplified theory is that if an individual purchases law enforcement services directly, the police are incentivized to serve that individual instead of the state. This does not imply that implementation of privatized services isn't complicated.

This also goes along with other principles, such as an extreme rejection of positive rights. A person isn't entitled to due process just for breathing where he stands, just like he isn't to food and shelter. It's up to the localized polity to decide if that person is permitted to travel or reside there in the first place, and whether to provide due process (or other amenities) or to expel him.

This post makes it evident that current systems de facto fall far short of reasonable ideals. We have a constitution that codifies natural rights, and a populace that forgot that it takes toil (negotiation with neighbors, companies, and other polities) or blood to guarantee those rights. Other comments here provide good policies (including acknowledgement that cost-effective capital punishment is more just than prison in many cases), but don't fully address some root issues of why our judiciary is so contemptible.