Well it depends on where it is built and when IMO. Like someone else said, the Empire State Building is special because of it's iconic status and it is in what is more or less the capitol of the world, New York City.
Take a look at the Dubai Marina supertalls. In 20 years, who will remember those? There's too many of them, they're so close, and they all look more or less the same. Those aren't that special.
In addition, all of those random supertalls going up in cities no one's heard of until they got on this site and saw a new proposal or something under construction and look at that city and have never seen it before. Those aren't that special either.
Really, it all depends on what the skyscraper stands for. Let's take the Jin Mao Tower in Shanghai for example. 421m, 88F. One of China's first supertalls, built in 1998. It is "the Empire State Building of China". Was once one of the world's tallest. Now take a look at a building of similar height, DAMAC Heights in Dubai. 420m, 85F. To be be built in the Dubai Marina, a supertall among supertalls.
Height is nowhere near everything, like many of these developing cities/countries are seeming to think. This is why skyscrapers like the Chrysler Building, Bank of China Tower and John Hancock Center will always be more "special" then these megatalls going up, like the Ping'an IFC, or the Golden Finance 117, or any Marina supertall.
So to answer your question: yes. Skyscrapers and supertall skyscrapers are becoming less important these days, when everbody and their mother has one.
If I am coming of as elitist, city-vs-city, or otherwise rude or ill-mannered, my apologies.