Good points. A 737 costs about $90M and seats about 162 people. Let's say it lasts 10 years and does 4 journeys per day, that's 14600 journeys in its life. So $38 per journey is needed to pay for the plane. A train costs $15M and has about twice as many seats. So, yeah train wins.

According to https://www.withouthotair.com/c20/page_121.shtml Trains are about 8.5x more energy efficient than planes. So yeah, trains win that too. For context, planes do about 80 MPG per passenger.

On the other hand, building HS2 might cost £75 billion. It might carry 100 trains per day, so 32000 passengers per day, if all the trains were full. That's 11.7M per year. If it runs for 25 years without costing anything more, that's 292M passenger journeys, so £256 per passenger journey.

I _think_ that demonstrates that the infrastructure costs are larger than the costs of extra energy requirements and airframes. But we're clearly into "it's complicated" territory, so I concede.