Many shows that have long runs often lose their direction and creativity and only remain on the air because of nostalgia. The Late Show with David Letterman is an exception to this rule. While shows like the Tonight Show with Jay Leno stayed on way past their expiration date, Mr. Letterman remain consistently funny his entire run. When The Late Show ends its run TV will be losing one of its greats.
There are very few enshrined names in late night TV, and even the ones long before the current generation get remembered. Johnny Carson, for instance, is instantly recognizable as a name, face and voice. Letterman is distinctive, long-lived in the industry and incredibly well known. The time he hosted the show will easily be remembered as one of the greats.
There have been, and probably will be for a long time, many imitations. But nothing beats the original. Stephen Colbert is the best possible replacement, but it will take a long time for fans to get used to him. The blend of the serious and humorous isn't one that every host can pull off right away, but Letterman did it with ease - nobody else willl ever do as well without being, to some extent, an imitation.
The late show with David Letterman has had enough of a following to remain a late night fixture for 30 plus years. In 1996 David Letterman was ranked No. 45 of TV Guides Greatest TV Stars of All Time. Viewers have been entertained by the shows unique style of late night comedy for decades and Letterman has survived scandal and health issues still to remain one of late night TV's top shows.