In early February, Stephen Colbert got a valuable piece of television real estate that no other late-night host had ever received: The post-Super Bowl slot, and the benefit of a lead-in from the biggest viewing audience of the year.

It was five months after his ballyhooed debut on CBS as a replacement for David Letterman on “The Late Show.’’ More than 21 million viewers tuned in that Sunday night, nearly 10 times as many as Mr. Colbert’s usual audience.

And though Mr. Colbert was said to be pleased with the performance, it barely made a dent in improving his standing among the late-night shows.

Shortly after his Super Bowl show, according to two television executives with knowledge of the discussions, Leslie Moonves, the chief executive of CBS, began several private conversations with Mr. Colbert to express concerns about the direction of the show, and to address one glaring problem: “The Late Show” effectively had no showrunner — someone who serves essentially as a head coach for a show — other than Mr. Colbert himself.