I think sometimes the Austrian distaste for empirics has left libertarians too eager to construct theoretical expansions of the private sector instead of appealing to real world examples of private services in action. Here are a couple of examples that I think libertarians should use a lot more:
1) Turnpike trusts
The construction of the railways with private capital is the classic example of infrastructure being constructed, at an incredible pace, by the private sector. The private sector railways only fell into disrepair and then the clutches of government when they were wrecked by wartime use and poor maintenance.
However, the railways aren't the only example of the private sector managing basic transport infrastructure. Calls for the roads to be privatised may seem radical now but it wouldn't be without precedent.
In the seventeenth century the roads were the responsibility of parishes and in a poor state. With volumes of trade increasing they were being used more and more heavily and needed investment and proper maintenance. The solution was a libertarian's dream. Significant numbers of the most important roads were handed over to Turnpike Trusts that looked after the roads and charged a toll for their use. They produced a much improved trunk road network and played an important role in moving goods from canal and railheads in the early stages of the Industrial Revolution.
2) The lifeboats
An emergency service run successfully for hundreds of years on a charitable basis, in the libertarians' dreams surely?
The Royal National Lifeboat Institution runs an emergency service that saves 22 lives a day. Running a lifeboat service is obviously a massively capital intensive activity and one that needs to be on service permanently. Despite that it has been a private service funded philanthropically since its founding in 1824. While the Admiralty could not be persuaded to take an interest private society set the service up and legacies and other donations still provide it with the funds it needs to operate each year.