That's a common misunderstanding. Very common.
In cruise mode Concorde was as efficient as a Boeing 747.
When you go faster, you do two things: 1. reduce the angle of attack, 2. fly higher. Concorde was flying twice as high as subsonic jets. The end result is that you still get increased drag, but much less than the square (or cube) of velocity would suggest.
Ok, but increased drag it is, right? Right, but you go faster. If your drag goes up by a factor of 2, but your speed by a factor of 4, then in the end you burn less fuel. It so happens that Concorde's drag went up virtually by the same factor as its speed.
The problem with Concorde was that it was horrible aerodynamics during the takeoff stage. At that point the plane is the heaviest (its has full fuel tanks), so the problem was compounded by some sort of "tyranny of the rocket equation".
Can Boom solve this problem? My guess is that this was their pitch to investors. In the 50+ years since Concorde was designed, both computers and computational fluid dynamics experienced huge advances. The computer I'm writing this on has probably performed more flops since I started writing this comment than the entire computational modeling for Concorde in its decade-long work.
As for military engines (and their maintenance) being expensive. F-35 is like a Formula 1 car, as USAF general Charles Brown once said. Its engines are pushed to the limit on a constant basis. A commercial jet is very different. It does not need to pull huge Gs. Its trajectory is very, very predictable. I'm sure a company like GE could make a very cost efficient jet engine for Boom. It's just that they have much better ROI if they build engines for F-35.
