Investment in public services is guaranteed, while governments can keep their budgets in order.These were popular in the construction of railroads in Europe and Latin America in the 19th Century, and governments lost a lot of money on them. (Just one nugget from the railway conference. Has to be a thesis in there somewhere.)
In the United States, the promotion generally took the form of land grants, and those didn't work terribly well either. The unsubsidized railroads such as Hill's Great Northern, and Hill's colleagues' Canadian Pacific tended to be more profitable. The one public-private partnership that turned into a serious money machine was The Pennsylvania Railroad.