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.
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.
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.