Actually, I suspect the internet has all but killed the real value of the Concorde.The only thing it had to offer was NY-London in 3.5 hours instead of 7.5 hours. There are so few cases where those 4 hours make any difference, particularly with the advances in telepresence, that there's just no real market for the service. The seats are all technically First Class, but First Class in a Concorde was really not that much better than coach in a subsonic aircraft. Personally, I'd take an 8 hour flight in a 747 with a seat that lays flat rather than pay the same price for a leather coach seat for 4 hours.
747 seats didn't lay flat at the time but, to your basic point, the real market for the Concorde--such as it was--was the international lawyer who had to jet over to London for the day. And it was relatively cramped compared to first class on a 747 and certainly compared to today's wide bodies. I'm not sure how much the Internet has to do with it as the Concorde never really did have a market but probably the "need" for 4 hour trips to New York or London have declined in any case.
Sure but to the ultra rich the Concorde lets them wake up and decide they want to eat dinner at the best restaurant in London that night, then fly back home to party all night in NYC.
Except not really, that's still 7 hours of flying. Lets say 1 hour transit from airport to restaurant and 2 hours of eating, you've already spent 11 hours on that dinner.
1 hour transit time to the airport? You need to get a new helicopter pilot.
Seriously though, you're forgetting timezones. Hop on the jet at 11am NYC time and be in London at 7:30pm London time. Leave London at midnight and be back in NYC at 10:30pm NYC time. You're not going to be exhausted from travel because it's first class all the way and you don't even need to pack bags.
Many bigger cities seem to actually be surprisingly lacking on viable (and legal) landing sites for helicopters... Trust me, I've tried.
You may not be exhausted but sitting stationary for 7 hours just to get dinner doesn't seem like such a fun thought, even in first class. (The novelty wears off very quickly)
Security is hardly an issue flying privately, I've had experiences where we've landed and all stepped out of the plane just looking around the airfield waiting for someone to come say something... and nobody coming.