The cost between any two cities on any route must < the cost of a direct flight between these two cities.
Well, that's easy -- both modes are heavily subsidized so it's just a matter of the government turning knobs.
"New Deal" build-up of rail, has knock-on effects
What actually happened: In WW1, railroads were nationalized. In WWII, railroads convinced the government not to nationalize them - but they were in crush overload conditions, and Pennsylvania Rail Road management "peeved off" General Eisenhower big time. Eisenhower built the Interstate freeway system to remove the military's dependency on the railroads. Eisenhower knew it would bankrupt the railroads, and was happy for that. Meanwhile, fast electric interurban railways were dying off pre-war. The "New Deal" was partly projects to create jobs - but on infrastructure projects that will pay economic dividends for decades, such as the TVA dams, Hoover Dam, Golden Gate and Bay Bridges, etc.
The US railroads ask Roosevelt to prioritize rail infrastructure to prepare for the inevitable war. Roosevelt agrees (Optional: on the condition that the railroads be nationalized again in the event of war.)
As a result, railroad infrastructure is a big part of the New Deal. It is ready and able to handle the nation's war needs. Pennsylvania Rail Road gives General Eisenhower 5-star concierge service. (Optional: The railroads are nationalized and Eisenhower is put in charge. Eisenhower sees it all from the other side of the fence). Eisenhower becomes pro-rail, and as President sees ways to improve rail further, and invests in rail instead of the Interstate system. This is the seed of American high-speed rail.
Notably, the interurban electric railways were on their last legs in the 1930s, but the New Deal re-investment in rail breathes new life into them and positions them to be the prototypes for electric high speed rail, with incremental improvements to their infrastructure - pantographs, weight-tensioning existing catenary, grade separation and alignment upgrades, voltage bumps. The former 600V single cars that bounced down the line at 75 mph now are fine modern 1500V 2-car sets cruising 125 mph on good rail. That's just the interurbans, obviously Big Rail aims much higher.
The Shah of Iran aspires to a constitutional monarchy
The Shah admires the constitutional monarchy of Britain, and adopts this at home. Which tickles both the Shah's American backers, and the domestic critics. Senators Khomeini, Khamenei, Banisadr etc. all work within the system instead of fomenting revolution - two of them having turns as Prime Minister.
The Shah thus becomes an influencer rather than an administrative leader, adored by the public throughout the Middle East. The Shah is highly influential in the Middle East, forming OPEC much sooner, and convincing many of a core belief: That oil is simply too valuable to burn as fuel, and should be reserved for its ability to create plastics and fertilizers. The Shah leads the Middle Eastern Nations to not "give away" their oil -- they treat their oil as a precious, one-time national asset. This has a huge impact on the price of gasoline and diesel. It remains a strategic national asset for every country that has it - not to be wasted on bloated 7 MPG personal automobiles with V-8 engines. The post-war automotive boom does not happen.
As a result, national investment goes elsewhere.
Many of us confuse "Progress" and "car ownership". But you have to look at a few things about the automotive life which are a constructive total loss. The life cycle of a car - building it, maintaining it, getting the fuel for it, building the roads for it, scrapping it - all of this is capital investment gone in the end. Like a candy bar, it gave someone pleasure for awhile, but it's gone now.
Are cars essential for some sectors and in some locations? Sure. But in the most highly populated urban locations, cars are hardly necessary and even get in the way. People only want cars because public transit is rubbish. Chicken and the egg. We need some, but not near so many as we have.
Another constructive total loss was "white flight" to the suburbs. You already have a perfectly usable building. Building another one while letting that one fall to ruin is a complete waste of material. Yet that was the fate of many cities from the 1950s to the 1970s, because of 12 cent gasoline.
Now, these constructive total losses do not happen so much. But that doesn't destroy the economic value of building that car and suburb -- much the opposite, the economic value is simply redirected into other things - things which may have enduring value.
For instance I could see the electronics revolution happening sooner. Strides might be made in healthcare. Electronics. Social equality. Renewable energy. Progress. Certainly, given this economic power that was created due to less cars, "high speed rail" is pretty much couch-cushion change. Just look at France, who can easily afford its first-rate high speed rail system.