Wake up at 4. Take the subway to the train station at 4.45. Reach the train station at 5.15, half an hour earlier in case of subway problems, and walk through the statin to fund the platform. Take the 5.50 train, reach the airport at 6.35. Check-in at 6.55. Go through security early, queue 40 minutes because it's Monday morning, it's 7.35. Submit yourself to the random terrorist check because you look like below 30 years old and in a hurry. It's 7.50. Run through the airport because you're at gate 167. You get your flight and be at work by 2pm, babbling because you woke up at 4 and sweaty because you've almost missed your flight. You'd believe you could reduce the margins for the subway, train, check-in, morning queue and terrorist check, but since you never know when they happen, they might happen all at once (anecdotic experience: I almost missed a SYD-LON flight and I systematically get terrorist-checked), and you don't want to come back to your boss saying you've missed your $3000 flight.
Get driven to the airport in the limo, express check in and security checks for first class passengers, quick coffee/breakfast in the first class lounge and board at your leisure, arrive at work happy and relaxed... That's why Concorde worked.
Concorde tickets, adjusted for inflation, often ran around $8-10k. No Concorde passenger would be taking the subway/train. They would use a fast private driver -- chances are they could even get some shut-eye in the car.
After too much international travel, I like the idea of taking a sedative and have your staff ship you comatose as cargo so you just wake up fully rested in bed at your new location.
I suspect this is a lot like surgery. Less anasthetic and more activity means you're physically healthier when you get done with the process, even if it's more painful.
The user experience would be like teleporting making an Uber feel prehistoric. When its that good it could be irresistible despite drawbacks like... chance of death and such.
So in other words you're travelling even faster. I'm almost certain that if Concord flew today you'd get express security (even "premium economy" gives you that for international flights). Also in some places taking the train is much faster than driving due to traffic.
At both Heathrow and JFK you boarded British Airways's Concorde flights from Concorde Room, a premium lounge with a directly attached jet bridge to the plane. (These live on as BA's lounges for first class passengers; even at Heathrow Terminal 5 from which Concorde never had a chance to operate. But they're nothing special. Lufthansa operates a dedicated terminal for their first class passengers at Frankfurt.)
In other words, ground services were and are a key component of a premium travel offering, and can effectively shave a ton off the total travel time. Concorde flights predate the now-common practice of bundling chauffeured limousine rides with premium airfare, but you have to expect that the average Concorde passenger had adequate arrangements in place for their airport transfers.
I've only flown Concorde in the easterly direction, with none of the "chase the sun" appeal. But if you're accustomed to the drudgery of the regular JFK-LHR redeye, a breakfast in Concorde Room at 8 am, a very nice lunch at Mach 2.0, and wheels down in London before 5 pm is comparatively a very agreeable way to spend the first half of a work day.