You've completely overlooked a huge element of the railroad business, too. While railroads may have competed for passenger traffic between cities, any one railroad customer located along a railroad could only do business with the railroad that served the customer directly. The Pennsylvania Railroad couldn't haul coal from mines that were served by the Baltimore & Ohio, for example. This is a monopoly arrangement by definition, and Federal regulation of the railroad industry was implemented as a measure of relief and oversight for railroad customers who had no alternative means of transporting their products.
Conrail and Amtrak were not "imposed" on the industry. The Federal government assumed ownership of the assets of six major Northeastern railroads that had tumbled into bankruptcy and were about to be dissolved. For better or worse, the Federal government (correctly) believed that a disposition of the assets of these companies would result in the sale of their rights-of-way. In addition to the threat this presented to the industrial customers of these railroads, there was no way these rights-of-way could ever be re-established once the properties were sold off.
I don't know where you get this idea that these railroads ever existed as truly private entities at all. The entire industry owes its existence to massive government intervention almost since its inception -- from land grants, low-interest loans, and special preferential treatment by governments all over the country (exemption from property taxation, for example).
Multiple railroads could serve a customer even with one railroad line of one company serving it directly; this was under track-sharing agreements.
Also, with government-financed roads, regulatory preference was given to trucking companies going way back to the teens and twentiestruckers could set their own rates whereas not even an interurban electric railroad could, and electric interurbans were intrastate for the most part.
The canals were like the railroads, a mix of private affairs and government builds. The Morris Canal in New Jersey was a major private canal that linked the Hudson River and New York Harbor with the Delaware River.
Yes, Conrail and Amtrak were impositions. Instead of removing taxation and regulations to allow the private companies to compete better, there was a federal takeover, which resulted in a far smaller railroad network that is today overburdened. Conrail could not be re-privatized without such legislation as the Staggers Act, which deregulated the railroads partially. Increase of regulation continued on the passenger rail side, which is why trains like the Acela Express ended up twice as heavy as high-speed trains of overseas (or US-built ones of the past).
Completely false presumption that all US railroads resulted from land grants. The Great Northern is an example of a railroad that came to be with no government intervention whatsoever.