More to the point (at least according to Bill Carter) Conan didn't want to do the commercial.
Conan O Brien applied for a job as a writer for Letterman around 1986, and was apparently seriously considered. When Letterman was reminded (years after the fact) just who he'd turned down, his response was "Well, our loss."
Possibly the biggest 'What Could Have Been' ever.... The Tonight Show starring David Letterman.