For whatever reason, it’s odd to think of Death Cab For Cutie as a stalwart of stadium rock. And yet Kintsugi, released in March this year, is their eighth studio album. Of Monsters and Men, who owe a clear debt to Death Cab, followed them on to the Amphitheatre stage at Splendour in the Grass on Friday night. Talk about being confronted with your legacy.

A not-quite-euphemistic reference to Death Cab For Cutie being “among the most established” of this year’s festival’s line-up obviously struck drummer Jason McGerr earlier in the evening. He sort of laughed. “Established, yeah. 17, 18 – 1998 was the first record. But hey,” he knocked on the picnic table he was sitting at, “I am constantly counting my blessings and thanking whomever, mostly the fans, that we’ve been able to do this as long as we have and stay somewhat relevant.”

The bands that he grew up listening to, like the Rolling Stones, U2 and Led Zeppelin, were “career-oriented bands”, he said, built to last. “The fact that we’re at eight records … why not go for 20?”

By McGerr’s own ruling, that’s the lens through which to view Death Cab For Cutie’s set, but none of the three bands he referred to are an easy comparison to make to Death Cab. Coldplay peddle a similar brand of introspective but stadium-friendly anthemic guitar rock – but they’re contemporaries, not something Death Cab can aspire to. Is this what it means to be in the waiting room for the rock’n’roll hall of fame – not a newcomer, not yet a legend?

They open their set with The New Year, the first track on 2003’s Transatlanticism: blazing guitar strums that burn brightly before giving way to tinkly introspection. Flanked by McGerr, bassist Nick Harmer, and touring members Zac Rae and Dave Depper, frontman and lyricist Ben Gibbard is a compact, curt figure on stage, taking up no more space than he needs to, and keeping the between-song banter to a minimum. In some cases, the song has barely ended before the next has begun.

But a pacy professionalism is to be expected after close to two decades in the business. I Will Possess Your Heart is eight and a half minutes long on 2008’s Narrow Stairs – and surely more tonight – but it still doesn’t feel meandering. Too long, yes, but purposeful. But to a large extent the setlist, the surroundings, the sound, even the more intoxicated members of the audience are beside the point.

It’s clear from the rapturous, tense reception of many in the audience that this is a band that means something to people – precisely what, maybe even Death Cab themselves don’t know. But that’s what happens with songs that capitalise on “the human element”, as Gibbard repeatedly refers to the guide for his songwriting in the program for Splendour: Death Cab’s back catalogue is full of tiny (or seven-and-a-half minute, whatever) vessels for the elements that make you human.

It’s impossible to listen to the band skip through Soul Meets Body in an amphitheatre in a field on the east coast of Australia and not be reminded of listening to it on your pink iPod mini given to you as a combined Christmas and birthday present, meticulously applying the lyrics to your relationship at the time. That’s not a bad thing, but it does complicate any critical assessment of their performance.

What do you make of a song that reminds you so keenly of a person you once were, that transports you so neatly back in time? Was it the same for fans of the monsters of rock today as they watched their teenage favourite enter the canon?

Backlit with blue, Death Cab’s performance reaches for poignancy and succeeds, the setlist striking the delicate balance of appeasing the crowd with old favourites while standing by their new material. But, as long as they played the songs mostly true to how they sound on record and no one went on a racist tirade or anything else that would have prevented the audience from retreating into their own pasts, it didn’t really matter.

Just as it starts to spit with rain, Death Cab For Cutie close their set with the title track from Transatlanticism, with its outward-circling, swelling outro of “I need you so much closer” capturing all the earnestness and introspection that fans love (and cynics love to ridicule) about the band – because of course they had to, because that’s what the crowd was there to see, that’s what was going to take them where they wanted to go.

• This article was amended on 27 July 2015. The original said McGerr was a founding member of Death Cab For Cutie. In fact, he joined in 2003 in time to play on the band’s fourth album, Transatlanticism.