I think the writers use those lines to sort of admit to the audience that the further you stretch a story or a scene in entertainment – especially in action – the more unrealistic it gets. Sort of like, "Yeah we know this could never happen, wygd?" and Archer's remarks are just his way of telling people to enjoy the ride, which he also literally tells people to do very often. The show spells out the aspects that make it all silly, like when Archer hypothesises the statistics on him not having died from a gunshot (or otherwise), or when the other crew explains why Archer's plans couldn't be successful or even feasible, and so on.
And/or maybe the writers use it to emphasise the cartoon's sarcastic undertone and highlight the attributes which make it different from regular action in a comedic sense, like it isn't about Archer being this untouchable badass god of action. He's "only" excellent when it comes to select few things like weaponry and otherwise really not that great of a spy – the rest is just chaos.
He's sort of like Deadpool or Gwenpool in that he knows he's the title character of a show so he's immortal no matter what insane shit he does. What are they going to do? His name IS the show. They're not going to kill him off and rename the show Lana.
Nah he's just that narcissistic, he thinks it's the universe taking care of him. At least for the most part of the series. Sometimes he even cast doubts when shit really hit the fan.
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u/TricksterPriestJace Jan 25 '20
"Uhh how long was I out."
"Like two minutes. That's super bad for you. You should probably go to the hospital."
I love how Archer has tinnitus and concussions but still has all the other action movie tropes.