Getting out from under the pile of bricks without any acknowledgement or curiosity about what just happened
Their utter indifference towards all the bizarre things that happen to them is a great running gag. We're not supposed to think "Oh wow, these guys are so cool", it's more that they exist within this weird, impervious bubble.
They're not cool in the comically heightened Fonzie sense, they're depicted as shabby, likeable losers: a wee fat bloke and a gangly nerd who inexplicably front a shit-hot rhythm and blues band. Aykroyd and Belushi sincerely adored that music, but I very much doubt that either of them ever thought of themselves as anything other than geeky enthusiasts who weren't fit to touch the (tremendous) hems of their idols' garments.
The film would be unbearable if it was just a couple of earnest white blokes saying "Now this is REAL music, folks." It's not that at all, it's an energetic and eccentric tribute to the life-affirming spirit of soul music, rhythm and blues and rock and roll.
It's also quite gritty, aesthetically speaking. Just look at the abject misery of Elwood's one-room apartment; despite being a big, wacky comedy, it's still rooted in '70s New Hollywood neo-realist gloom. That doesn't work against the comedy, Landis made it work to his advantage. It's a very funny, silly film, but it's mired in oil and dirt.
Sorry, I've written far too much about The Blues Brothers in this thread. It's one of my favourite films, so I'm prone to droning on about it.