US audiences have watched Letterman since Late Night premiered on NBC in 1982, where his absurdist streak subverted the talk show genre perfected by Johnny Carson.

Letterman then evolved into the elder statesmen who – throughout his controversial switch to CBS – carried the torch as the undisputed King of Late Night. With his favourite guests (Bill Murray, Julia Roberts, Barack Obama) swinging by to say farewell, and Dave commissioning musical numbers from performers he admires, the final episodes have been crushingly sentimental.

Even gags wheeled out annually had an unexpected last-hurrah poignancy: ("It's the Dog Show and Fashion Week in New York City. I tell ya, we've got bitches coming and going.") In Letterman's own words, "Everything must go".

In the fall of 2005 I was fortunate enough to intern in the writing department of the Late Show with David Letterman. Televised five nights a week since 1993 from the Ed Sullivan Theatre on Broadway, the Letterman marquee has been, for me, the mecca of show business.

Being granted the opportunity to see up close my comedy idol, and soak in the talent and professionalism that kept the program humming, was a formative and profound experience that continues to shape my approach to the hard work of making comedy.

When I did meet him, which is rare even inside the building, I was evidently more nervous than I thought because I turned around and immediately walked into a door.

Despite the inauspicious introduction, and the position being unpaid, my time in New York was, without a doubt, totally worth jeopardising my parents' retirement.

An abiding impression is the sheer effort, passion and attention to detail required to get such a monumental production to air and, moreover, make it look easy.

When Letterman galloped across the back of the stage at the start of each show, his silhouette was not just an eccentric trademark but symbolised the nervous energy that builds before a live performance. The ritual was testament to the esteem in which he held the gig, despite over three decades helming more or less the same format.

While the taping took place, the writers upstairs would work on the following night's program, a sausage factory of comedy that lasted over 4000 episodes and churned out a cavalcade of writers, many of whom kicked on to create their own TV shows and movies. The "Top 10 lists" delivered to his office would return annotated in pen; his handwriting improving upon the material provided by his writers.

The day I saw one of my jokes made exponentially funnier by his hand remains a surreal career highlight.

It's natural to reflect on the big guests and iconic moments but, for me, Letterman's magic lies more in his ability to elevate the disposable into the dynamic. Segments that in anybody else's hands would be a huge waste of time were, filtered through him , imbued with comedic possibility.

To take one example from thousands, 'Non-surviving Survivor' contestants booted off the reality show were denied an interview at the desk, and instead relegated to being quizzed by staff members who wanted to know, "Did you see or touch any monkeys?"

Letterman managed to fuse his network obligations with irreverence to create content that – against all odds – was worth staying up for.

From the beginning, Letterman was an endearing crank who demolished the prevailing idea that a host must at all times be shiny and likable. We tuned in not necessarily for the guest, but to see how Letterman would relate to a guest – any guest; their chat creating a unique frisson that stood out on the crowded promotional merry-go-round.

Appearing on the Late Show was a sign that an entertainer had 'made it', and so they saved their best stories, and outfits, for Letterman.

It was often clear when he veered from prepared notes, presumably to keep himself engaged, and if the person could keep up they became a show darling. Ratings would spike depending on the wattage of celebrity but rusted on fans knew that every interaction was potentially memorable.

Gold could be spun even when plans fell through. When John McCain pulled out from a scheduled appearance at the last minute during the 2008 Presidential election campaign, Letterman and his replacement guest, Keith Olbermann, made a mockery out of his excuse that he needed to fly back immediately to Washington by taking the live feed of the Senator having his make-up applied before an interview just around the corner.

As Letterman was fond of saying, "The road to the White House runs right through me."

What I will miss the most is Letterman's superb gifts as a joke and storyteller.

Before the taping of the show, he would spend a few minutes fielding questions from the audience, which – while not televised – inspired comedy riffs and anecdotes that would make him a superb talk show guest were he not busy as a host.

During the monologue, each gag was delivered expertly with a casual element of surprise, and his quirky ad libs during set ups were often funnier than the punch lines themselves.

Paul Shaffer and the CBS Orchestra added inconspicuous sparkle, accompanying Dave's jokes and gestures with sounds and effects that fleshed out the material and effectively made the band an extension of Dave's personality.

It's an impressive sleight of hand for a TV host to be on air every night for 33 years, share so much of his personality and life, and yet remain enigmatic.

We watched Letterman mellow after his heart bypass surgery and become more empathetic following the birth of his son.

In an age of increasingly niche entertainment, Letterman was an old-fashioned broadcaster who refused to play broad.

Thank you David Letterman, you are an inspiration and will be sorely missed. I'll see myself out.

Daniel Burt is a comedian and a staff writer for The Weekly.