Dick Cavett made the rounds when Carson past away. One of his stories was that he was writing for Carson, and having an off day, he came up with some pretty lame jokes.
Carson stopped by the office, and subtly let Cavett know that the jokes stank, and he expected better of Cavett.
Maybe Letterman's crew has a lot of off days, especially since they're all leftists, and are loathed to shoot any of the fish in the liberal barrel. That doesn't leave much of the social/cultural/political pie left as grist for the comedy neurons to spark with.
So you need a big pool of writers to find one that can write on any given day.
I heard that Leno or Letterman have or had dozens of writers. Sounds insane for a one hour show with a 5-minute monologue.