You could argue that there are positive externalities to building high speed rail that make the public funding worth it. For commuter trains it's reduced congestion and cheaper housing (allowing people to move to the suburbs). Thus a train service can operate at a loss while still making money at a societal level.
What purpose does high speed rail serve that isn't mostly covered by planes?
Sometimes you can drive somewhere faster than you can fly there, entirely because of all the setup and teardown implied by a flight. It’s this intermediate distance travel where high speed rail really shines.
I think thw biggest win would be in cities. People wouldn't need to take cars everywhere, so you build things more densely, etc.
The high-speed train between New York and Boston could make two or three stops, for example.
I think 9 million people travel between San Francisco and Los Angeles every year. Wouldn’t that be best served by trains?
As the US grows from 350,000,000 to 450,000,000 people, should we add a few more trains every day, or a few dozen airplanes?
If customers are unwilling to pay the asking price for an offering, the value proposition is off. Perhaps the model is bad, the price too expensive, or the terms old-fashioned. “The market” is individuals seeking mutually beneficial trades: greedy capitalists and greedy consumers. If the trades aren’t happening, the necessary mutual benefit is not present. Forcing people to render services or accept services for terms they wouldn’t voluntarily agree to is not freedom.
Yes, voluntary persuasion is hard work.
Then why does the US governement fund roads? Because there's a collective bargaining / coordination problem. It benefits us overall if we have them, but that doesn't mean that a profit could be usefully generated from maintaining them, or that this is the best way of running the system (we want to maximise use of the infrastructure, not discourage use with high usage tariffs).
The is fundamentally an economic argument, albeit one that recognises value beyond monetary value.