But I thought at least one of his predecessors, Steve Allen, had lots of jazz guests. Do you mean his two followers? yeah, they are too much into rock and not into exploring anything else.
I'm pretty sure he meant to type "successors"---and in that he's quite right. Jay Leno and Conan O'Brien are rock guys, which is hardly surprising considering the generations they come from. When Carson, OTOH, was growing up it was not at all unusual to be at least a little bit of a jazz fan. But Carson also had (thank God) an unusual interest in music, for a comedian. He was even an amateur drummer, which may explain why he had Buddy Rich on about a billion times.