Mostly just "thinking out loud" here...but I'm reading over this and wondering more and more if anyone can truly do a definitive ranking of ten top influences. Letterman influences Kimmel - Carson influences Letterman - a radio comic like Jack Benny influences Carson, Paar or Allen - and so on. A generation from now you'll find hosts who consider Kimmel or Fallon or whoever replaces Dave as their top influence.
Up front, I have to question whether even Carson is Letterman's greatest influence. I'd suggest that title has to fall to Paul Dixon and Rich King - a pair of Cincinnati broadcasters who Letterman watched, listened to and learned from while growing up in Indiana. And you cannot discount the fact that generational shifts in society have also influenced all the hosts of late night too.
Late night has been based on Pat Weaver's original template for NBC Television's Tonight. For the first 40 years, NBC had that time mostly to themselves. CBS may have tried to challenge with Griffin or Sajak. ABC with Bishop or Cavett. Syndicated with Bill Dana's "The Las Vegas Show" or Arsenio Hall. None had much if any impact against Tonight until maybe Arsenio in 1989. If a ranking of network level television influence can be done, I'd contend that only those early Tonight hosts with the genre almost exclusively to themselves must be counted as the top three. Working off Weaver's foundational template, they built the late night television genre. All that have followed, from Cavett to Dave to Arsenio to Conan or Ferguson or Stewart have only adapted Allen, Paar and Carson's build out of Weaver's template to the changing tastes of their generation's society.
So I guess that means that at best, Letterman can only be considered as fourth on the list. Cavett's ABC show tried, struggled and eventually failed to create a younger, hipper version of late night going head to head against Carson. Letterman was the first to succeed in creating that younger, more hip late night show. But could Letterman have been a success had he launched his type of late night show against Carson on ABC or CBS? I don't think 1982's 11:30 PM audience would have been ready for a show like Letterman. Dave might have ended up with Merv and Pat in CBS late night's forgotten past.
No...what helped Dave establish himself was his time slot. He replaced Tom Snyder's "Tommorow Show" following Carson on NBC. And yes, without Letterman's first success on the 12:30 AM "Late Night," I doubt if there would have been an Arsenio who could compete head to head against Carson for that younger audience seven years later - with the resulting call for a younger Leno to replace Carson ending with Dave's move to CBS. Did Letterman break new ground? Not really. Letterman only built a show for his generation on top of that original late night foundation. Certainly Dave is an influence - but no one, not even Dave, can surpass the groundbreaking influence of the early Tonight hosts.
And if you think about it, even the guys like Griffin or Cavett or Chevy Chase who failed in late night influenced by teaching what not to do. Those who have followed the early NBC pioneers have only adapted the basics. There'd be no Letterman, Stewart or Fallon without Allen or Carson building on Weaver's foundation. You see guys who adapt for a new generation...or who adapt by taking a show toward more absurd comedy or toward more serious talk. Would there have been a Conan or Craig Ferguson without Dave? Would there be a Jon Stewart "Daily Show" without Bill Maher's "Politically Incorrect?"
If a list can be done, you'll always have far less than ten who will be counted as the true top influences of late night. The rest may have some influence, but mostly the rest are just followers.