why don't we already have supersonic business jets (SSJBJ)?

They aren’t downplaying their planned capabilities:

LA to Sydney is 7500 miles - more than twice NY to London.

The Concorde was one of the few projects the incoming Labour government in 1964 couldn’t cancel. Although the French privately suggested later on that they would have liked to cancel as well.

The SST was a Tory idea?

I don’t follow UK politics as much as I probably should, but: Wasn’t this a tip-off that this was a pork barrel, not an airplane?
Or maybe they planned to paint Union Jacks all over them and use them a propaganda “Go, UK! Go!” billboards?

Another point to ponder - I recall from some discussions about aircraft - to go twice as fast takes 8 times as much power. Thus, the power of the engines and the amount of fuel is astronomical for SST flight.

It’s not quite as simple as that.

If, for example, a supersonic aircraft flies much higher than subsonic ones (where air density is less) it can do better than the above.

Yes. Quite awhile in development, but approved by the Macmillan Cabinet in 1962. It was as much about geopolitics as it was about aviation: Concorde - Wikipedia

That’s only if the Coefficient of Drag (Cd) and air density do not change - in which case air resistance increases as the square of speed. But the power required to overcome air resistance is equal to speed * resistance. (Because energy = force * distance, so power = energy / time = force * distance / time = force * speed). Which means if you double the power, air resistance increases by x4, and power to overcome it increases by x8. However, you get to the destination in half the time, so the energy needed for the trip is only increased by x4.

However, Cd is not constant. It increases as you approach the sound barrier, then goes back down. So traveling at Mach 1.2 would require much more than 8x power than traveling at Mach 0.6.

The other key is that even perfectly ordinary aircraft can still get most of the way to the sound barrier. A 747 can do something like Mach 0.85. Is the difference between 0.85 and 1 really worth it?

That’s what I was trying to get at with my post above- the faster business jets are already close to Mach 1, so you’d have to go significantly faster than that in order to make the extra cost and trouble worthwhile.

Didn’t see it mentioned but getting permission for the Concorde to land in New York was a very contentious thing. Eventually it got permission but I’d imagine similar opposition would happened today and the Concorde had the advantage of being built by two Allies so there was reluctance to get them mad.

Also the plane was incredibly noisy when it took off. In the 1980s I worked occasionally in Breezy Point, NY. When the Concorde took off across Jamaica Bay from JFK airport, you heard that thing. Never any other plane,just the Concorde. They couldn’t build it very large and the prices kept down demand to the very rich who had to get across the ocean quickly (like Phil Collins playing both London and Philadelphia the same day for Live Aid).

Staying habitually near Brookwood, Surrey, back in the day, the morning Concorde to New York passed overhead each day and you certainly knew it.