Simple analysis: you could only watch one talk show host for the rest of your life? Most people would choose Letterman. Carson was great and would get the "most accomplished" nod. But Letterman was more enjoyable. This is a bit of snob's argument. But ask any comedian - who was the best? Letterman will always be the answer. He is worshipped by most every comedian of the last 30 years.
Because of his ability, which by the way nobody esle has, to create such wierd situations in which often even the guest seems to be irretated about the crazyness of a question that its so unbeliveable funny and entertaining. He is even able to make the audience think he lost controll about the conversation and again creates a lot of fun by doin that. That what makes him the best.
He's not the best comedian or interviewer or whatever but he's a great satirist. He was really good at Carson, and he amused Carson. He inspired many comics such as Conan, Fey, Baldwin, Sandler, Kimmel, and so on. May be he's not as great as he used to be, but you've got to respect the guy.
Time is infinite. A common analogy used to illustrate how long humans have been on earth is to scale it down so that the Earth is formed in the first second of the day, and today is the last second. In this analogy, humans don't even show up until 11:58:43 PM. So in this frame of context, David Letterman can't be the best talk show host of all-time because there are millions upon millions to come yet and you cannot grade yourself against the unknown.
Also Conan is way better.
While David Letterman is a funny and talented man, he is not the best talk show host of all time. The very best talk show host ever is Johnny Carson. No one on the air today or in the past can beat Johnny for his comedic timing, his sense of the absurd, and just all around talent.
David Letterman is one of the best talk show hosts of all-time but I do not think he is the best. To find the best talk show host of all-time, look at Jay Leno. The man is funnier than Letterman and gets up there every night and tells funny jokes. His interviews are the best too.
David Letterman is clearly not the best talk show host of all time. That honor should go to Johnny Carson. Carson had the ability to interview a whole range of guests with intelligent comments and questions without constantly exposing his political views and staying unbiased. Carson also showed a myriad of talents for comedy, music, acting and other talents that Letterman does not have.