We should have the airport model were the Gov. builds the tracks and the stations and then bid out the rights to run the trains.
The European Commission requires each state to set up a track authority and to separate track from trains. The track authority is supposed to request demands for slots, which can be either freight or passenger. Each slot can have its price. This is implemented in different forms in different states.
Does it make sense? It's too soon to tell. In Britain the government went further and privatised everything, including Railtrack. This was a disaster when Railtrack contracted out maintenance to cowboy engineering companies and a number of serious accidents occurred. Not a good idea. A new company was formed which may or may not be state owned (probably it is).
Should the US do this? That's for your political system. If the government owned the tracks the problems of freight delays to passenger trains would diminish, perhaps. In Britain Network Rail controls the timetable and the slots. But huge investments would be needed.