Both airlines and highways are heavily subsidized, in different ways. Totally private passenger rail service beyond short-haul, high-volume commuter service really can't ever compete with them head-to-head.
Amtrak is a favorite GOP whipping boy, but it's a straw man, the GOP lards the budget with as many airport and highway project pet projects as the Dems do. The government runs Amtrak by default precisely because the railroad corporations found they couldn't run passenger service on a paying basis competing against buses running on Federal highways and airlines that don't pay the bulk of the costs of the things that keep them running like ATC systems, airports, nav system networks (supplanted by GPS mostly, but they don't pay for that either) or pretty much anything else except planes, aircrew, and fuel. The States, by the way, do tax the diesel fuel used by locomotives.
All the hatin' on the post office is equally ill-considered, it would not run cheaper or better if privatized; it runs about as fast as you can reasonably expect now, and if run on a totally commercial basis, first class mail would be about two bucks an ounce, minimum.
Both of these things are items many folk on the right put into a magical belief system, based almost entirely on faith instead of any actual analysis about the economics or policy reasons to maintain all three modes of transport.