The Concorde demonstrated the failure of the Mach 2 class airliner, not just because of "high fuel consumption" but because it could not do multiple trips across the Atlantic in a day thanks to takeoff and landing restrictions. Originally people thought the SST would crush all other airliners economically because they could fly twice as many flights in the same time ("half the capital cost") but that was not realized. (People in London and NYC have to sleep once in a while)
The Mach 3 class typified by military projects such as the SR-71 and XB-70 might be successful at both problems.
Believe it or not supersonic cruise at Mach 3 is about the optimum fuel economy for supersonic flight and it might be fast enough to do more flights and lower the capital cost.
One gap between the Mach 2 and the Mach 3 classes is that at Mach 3 you have to give up on aluminum as a structural material and switch to Iron, Titanium, or something else. The SR-71 squared some of the design circles by taking off with a minimum fuel load and refueling mid-air -- airliners would have worse problems in terms of wing design.
There is no commercial airliner in the Mach 1 class, the economics are certainly worse than Concorde. The Mach 1 business jet might just work if somebody values the time over the economics.