Johnny Carson had three rules about Late Night: 1) no full fledged monologue, 2) no announcer/sidekick and 3) only a small combo, no big band. As the years went by, Dave worked in some topical jokes to his "opening remarks", added an extra musician on occasion and started to banter with the bandleader (Paul Shaffer). Johnny was such a fan of the show that he never said a word about it, even though they were severely bending, if not breaking, "Johnny's rules".
I think Johnny eventually realized Dave's show was very different from his and wouldn't ever seem like a substitute for it with viewers. It didn't need any rules to make it that way. Dave's style was just different. Johnny eventually made a couple appearances on Dave's CBS show. He never appeared on Leno's Tonight Show.
Paul reading those letters against the nature backdrops with bucolic music looks a lot like what SNL would later do with Jack Handey's Deep Thoughts. Although Handey's Deep Thoughts first appeared on the NBC summer program Television Parts in 1985, before this Letterman episode.
Okay, I'm pretty sure this is the very first Letterman show I ever saw. I remember "Microphone Land". First saw Letterman's 5th Anniversary Special on a ski trip with family and neighbors. I was always told to go to bed there's nothing happening at night. Well then I discovered this awesome show! The fountains, confetti blowers, Thrill Cam! I loved it! By the way I've always groaned when George W. Bush said "nucular". Seeing Dave said that it's nuclear and not nucular.
I think this might be the year I started watching too. I remember that fountain showing up on a lot of episodes. One episode I clearly remember watching live was the one where Steve Martin can't throw a pencil through the window, which aired in July of 1987, not long after this one.
Also on that list of things Carson had stipulated: No old timey guests like Carson had on his show. Although, Dave had guys like Art Donovan, Bob Hope and so forth. But like you said, Johnny loved the show so much, he didn't bother.
