My understanding was that, even for BA, the Concord was profitable on a cash accounting basis (as in, the tickets more than covered the cost of fuel, salaries, etc.) but not when accounting for a) the depreciation costs of the plane, which were much higher than for an ordinary Boeing or Airbus passenger jet since it was a one-off limited run and there were few spare parts and b) as you said, training new people to fly it, since it was an antiquated plane without a glass cockpit and the skills did not transfer to other planes. That's why it got harder and harder to justify over time until it was shuttered after the fatal crash during the general post-9/11 aviation downturn.
It also had a three person crew, and post 9/11 was the start of structurally higher oil prices, both of which were a death knell.
The true nail in the coffin was the development of the lie flat business seat, which meant that you could cross the Atlantic in three hours in a plush but cramped seat, or spend less money to sleep for six on a redeye and arrive well rested. At that point three hours was not a compelling enough time savings, but the Concorde also didn't fly far enough to do routes where the speed resulted in more significant time savings, like on transpacific routes.
London doesn't even require a red-eye from NYC--or actually from Boston/Washington although it's a very early star--on a conventional jet. I've done it pretty regularly. Not pleasant but I can get to London in time for a late dinner.
Also, my understanding is that AF was not profitable on Concord even ignoring those accounting costs. So AF wanted to shutter the plane after the accident, and changing the costs of shared maintenance equipment from 50/50 to 100/0 made BA's numbers go into the red too, because it wasn't very much profit.
Yeah of course there was always going to be an end date. However, there are people saying it was not profitable at all and that is not really the truth.
Bannister knows probably more than anyone about the topic and tells the story well. Thoroughly recommend the book. His tale of a guy called Bill being invited into the cockpit and discreetly given the controls to fly supersonic was awesome. Of course, later over a beer Bill (Weaver) talked of his times flying the Blackbird at twice the speed, and of the time it disintegrated around him.
