I think that Concorde IS a significant plane because it was the result of an international dream to go faster. Seacue's points about the time advantages being lost in airport time , and traveling to and from the airport are good ones, and I think that the next generations of SSTs will probably be smaller.
However, Phil Collins, one of the greatest drummers in the world (and being a drummer I KNOW how skilled he is!), played a huge charity gig (Live Aid) in the afternoon in London, then another at the same time in New York, and this was watched by the biggest ever worldwide TV audience! This was a defining moment in world history, a huge chunk of the world'spopulation uniting to relieve a crisis in Africa, and for a major star to be able to do two sets at the same time in London and NY was a cultural and humanitarian event of monumental significance and precedence. Concorde did its part, and we all knew it. Has any other plane in history had such a large "virtual" audience, or played a part in such a huge rallying of humanity to a common cause?
The pros and cons of supersonic airliners, and the costs/efficiency/need are debatable. What is not debatable is that it was perhaps the first major International collaboration, effectively the start of Airbus which is now a major manufacturer, in fact I believe Airbus is now "bigger" than Boeing, and that too is hugely significant. When Concorde was being planned who in the world would ever have thought that Boeing would have a major challenger?!
Concorde introduced huge new technological steps, a "giant leap for mankind" if you like! When they were finally retired, it was reckoned that the air-frames STILL had 20 years to give, and despite the extreme demands of supersonic flight I find that truly staggering.
The last point that demonstrates to me that Concorde is of world-class important concerns an article I read about 10 years ago in Smithsonian Air and Space magazine. Once USA were given retired Concordes, teams of US engineers and technicians were studying them in exacting detail, and this A&S article was all about their investigation and how they were planning to use their findings. Once mankind has made a technological leap, that knowledge is there for all time.
Bums on cheap seats drives the airline business more than ever, internet reduces the need for supersonic flights to meetings, but time is still money and humanity has been driven for centuries to reduce travel time and Concorde is the defining monument of that quest.