I never knew I had much in common with David Letterman until his final show last night. Sure, we share a mutual appreciation of Bill Murray, and we’ve both been amazed by Future Islands’ chest-thumping dance moves. But what I didn’t realise is that our bond runs far deeper, as two people who’d proudly put Foo Fighters’ Everlong at the top of their all-time favourite songs list.

Everlong was the ideal song for Letterman to bow out on, not least of all because of his enduring relationship with the band. When he underwent quintuple bypass surgery in 2000, Foo Fighters played on his first show back, signalling his return. Then in October 2014, the Foos became week-long residents to celebrate their Sonic Highways album, the accompanying HBO TV series of which was boosted by Letterman’s Worldwide Pants production company.

But it’s also because Everlong doesn’t just pull on your heartstrings, it shreds them. As the montage of Letterman’s infamous moments rolled, Everlong’s visceral drums, soaring chords and Dave Grohl’s throaty bark could have coaxed emotion from a lump of iron ore. The song boasts enough heady twists and turns to keep fists pumping, a metallic tang that stops it being Coldplay-cheesy and an energy that could muster excitement from the hardiest Grohl-o-phobes.

Lyrically and sonically, it’s perfectly shaped. Everlong encapsulates that intense, wanna-drink-you love that, deep down, everyone, even serial Tinderers, wants to find. In Grohl’s own words, that means being “connected to someone so much, that not only do you love them physically and spiritually, but when you sing along with them you harmonise perfectly”. When you’re a 14-year-old from suburbia, as I was when I first heard it, you want to be the girl that’s “out of her head” and you want Dave Grohl to kiss your face.

Perhaps the best thing of all about Foo Fighters’ beefy ballad is that despite what it means to Grohl, its lyrics are abstract enough to accommodate whatever meaning you want. For me, it was the song I stuck on repeat when I’d been ditched by someone who wore baggy skate pants and a hoodie. It was the beating heart of my teenage mixtapes, the track that honked BE MINE PLEASE SEXY BOY as plainly as any Valentine’s Day card. It’s people’s first dance, breakup song and funeral dirge. For Letterman at least, its line of “you gotta promise not to stop when I say when” felt almost custom-made for his final Late Show moment.