What happened in the intervening decades is "air travel got cheap" rather than "trains got expensive" (though from a relative perspective, coming to the opposite conclusion on face value isn't unreasonable given how inflation works and how it's sometimes hard to really process stuff like that).
You are correct.
Since deregulation of airlines, airfares have dropped, as the cost of transporting one passenger one mile has dropped significantly. In part due to this, demand for air travel has soared.
The same thing has happened with freight railroads: since deregulation, the costs of transporting one ton of freight one mile has dropped significantly, as have rates. In part due to this, demand for freight rail has increased since deregulation (although precision scheduled railroading has reduced rail traffic).
The private sector and deregulation are far from perfect, and there are many grounds to criticize them. But if there were a way to have passenger rail provided in a deregulated market by the private sector, the experience of airlines and freight railroads suggests that costs and ticket prices would fall and traffic would rise.
At a minimum, I would think that passenger rail in this scenario would have much lower onboard staffs, longer trains and more use of technology to replace labor, and more efficient equipment, as airlines and freight railroads have done.
If only there was a way to ensure long-term profitability of privately-provided passenger rail, I think we’d have a very different system.