Concorde was at least partly a remnant of people flying to London to close a deal over lunch and getting back to New York in time to tuck the kids in. I assume that sort of things is at least less common today.
The innovation that killed Concorde was the lie flat business seat. You could be cramped in the Concorde’s leather bus seat for three hours, or you could save money and get a sleep in for six hours.
BA and AF managed to keep the zombie fleet going very profitably all the way until the end in the early 2000s, and that business wasn't killed by the lie flat business class seat either. It was killed by the impossibility of continuing to operate a tiny fleet of '60s planes forever.
Now if you said that the reason we don't have ANY supersonic passenger jets today is because lie flat business seats are good enough, then that's a more defendable position, but I'd still say that the overland flight restrictions limiting any SST to just a couple of routes is a bigger factor.
When I flew on Concorde the one thought I never had was "I wish I had a lie flat seat and half the airspeed".
A six to three hour flight is not really worth the premium. At the same time no supersonic flight has the range to do transpacific where the time difference would be much greater.
The extra $4K or so in your pocket pays for a lot of reduced comfort for 10 or so hours.
A schedule I found was:
BA002 dep JFK 08:30 -> arr LHR 17:15
BA003 dep LHR 18.25 -> arr JFK 17:00
Still, certainly allowed "oh crap, need to get to london to do some very important same day business (and return the next day)"
BA 001 LHR-JFK 10.30am arrive JFK 9am
BA 002 JFK-LHR 9am arrive LHR 17.25
BA 003 LHR-JFK 18.25pm arrive JFK 5pm
BA 004 JFK-LHR 12pm arrive LHR 8pm
A same-day return would be useless as you'd have only 3 hours at JFK.