I remember seeing an interview with him many years ago (probably late 70s/early 80s.) He was offered his own talk show, but absolutely refused to compete in the same time slot as Johnny Carson because he felt he owed his career to Carson, and it would be an act of betrayal to compete against him.
First, at the time, NOBODY would have been able to match Carson's audience.
Second, Carson was very sensitive regarding people who he thought his show made them "stars".
IIRC, when Joan Rivers tried to start her own show, Carson never spoke to her again.
He thought she was being an ingrate.