Why it's cool (other than being funny): The voice shows he's already thought about how each bit is being perceived by the audience. So it's clear he's got total control of the stage and the room. Also, it totally disarms anyone who might get offended by any of his bits (he's pretty clean generally but there are a few jokes he does that toe the line). I feel like it's Gaffigan subliminally saying, "I get why you might find this joke stupid or offensive, but you don't wanna be the real-life version of this lame character I'm doing, do ya?"
In this interview, he explains how he came up with it:
It was a character that I did that was always part of my personality. And I still will do it in everyday life. If I'm late to meet my wife, I'll be like… [Inner voice.] "I can't believe you're late." I used to do it at this place Surf Reality on the Lower East Side of Manhattan. But during my Comedy Central Presents, I made a point of not doing it, which seems kind of odd, but it is something that certain audiences wouldn't get. But it's something to keep the material fresh. I remember being in DC and hanging out with Dave Attell—he was the headliner and I was middling—and me just going crazy with the inside voice, 'cause there is an improvisational kind of side to it. And it just really clicked. Attell was like, "Ah, you found your gimmick."
I think it's fascinating to watch how many angles he can take on a single topic too. Comics like Chris Rock, CK, or Paul F. Tompkins are great at wringing a topic dry. But I don't know if anyone attacks a subject with as many quick jokes as Gaffigan does. Just one-liner after one-liner. He builds a rhythm and then keeps hitting for minutes, even after you figure he must have exhausted every angle on the topic.
That's why watching him do, say, a whole Letterman spot on bacon is so fun. Or his classic Hot Pockets routine:
That much material from such a silly topic is a whole joke in its own way.
He stopped in at a show at Ochi's Lounge last week. His latest target: Dunkin Donuts. He's got good stuff brewing on that topic too. Also fun to see that he keeps all his jokes in a couple of binders that he carries around in a backpack.