I'm all for private operation of such systems to assure efficiency.
However, to be competitive with other modes of transportation (roads, highways, airports, etc.), the original construction costs must be similarly subsidized.
It's how transportation infrastructure has always been developed in our nation. It is a legitimate function of government, and you'd be hard pressed to name any major transportation system that hasn't required major government involvement: roads, highways, bridges, tunnels, canals, locks & dams on our inland waterways, airports and the air traffic control system, the original railroads, etc. etc. etc.
Private sector purists are merely obstructionist idiots.
Private sector would probably get things built cheaper, better, without the Union due or built in graft for inferior product. It'd also do away with politicians taking our taxes for build the roads, then putting toll boothes on them despite immense public outcry like they are doing here in Austin.
If the private sector can build huge skyscrapers and sports stadiums, mixing tar and dirt for roads should be a snap. Just because "that is the way it has always been done" does not mean that other ways cannot produce better results.