I don't know why people think fuel costs are a problem. BA was reporting making piles of money on the Concord flights. Obviously seats aren't going to be cheap but as long as people are willing to pay more than the fuel costs their seat costs and as long as the airlines can fill enough seats to maintain a viable schedule, what does it matter?

The real problem is that Concord was 1950s technology. The people with the technical expertise to maintain it, fthe people with the expertise to fly it, the suppliers for the parts it would need, and anything else it would need to run would be a herculean effort to source. And for that effort you would get a plane that didn't meet modern expectations for service (food, comfort, space), produced more noise than airports are willing to deal with, and would lack the modern safety devices that are expected today.

The situation is not unlike classic cars like the Mini. You can keep driving the old cars as a one-off but you're not going to put a lot of miles on them and the comfort, safety, and reliability will never match a modern car. If you want to produce a marketable version of it you'll start fresh with modern technology and make a new set of compromises and tradeoffs.