Has the V&A gone a veteran rock group too far? Will its Pink Floyd exhibition next year put the public into interstellar overdrive or leave us comfortably numb?

This grand old Victorian museum has sensationally expanded its audiences and horizons in recent years with exhibitions dedicated to Kylie Minogue, David Bowie and – opening on 10 September – the great psychedelic rock age of the late 1960s. While Kylie may be regarded as a camp fashion-pop detour, David Bowie Is... proved a massive critical and cultural success, helping to generate a timely comeback for the star and enthusiasm from artists who count among Ziggy’s most passionate admirers.

Bowie, in other words, had credibility as art – heck, he was Britain’s Andy Warhol. The music featured in this autumn’s You Say You Want a Revolution? is similarly cool, not to mention steeped in artistic associations from Warhol’s Factory to Antonioni’s Blow-Up. But Pink Floyd? The monoliths of the concept album? The titans of grandiose stadium pomp? Is a Pink Floyd exhibition art? Is it even style?

The Floyd’s most dedicated fans would have to admit that their cool phase and involvement in contemporary art ended when Syd Barrett left the group in 1968. The Lewis Carroll-tinted psychedelic whimsy of early songs such as Arnold Layne and See Emily Play soon gave way to the melancholy cod-philosophy of Roger Waters’ lyrics, while the band’s innovative 1960s light shows (undoubtedly reflecting the experimental art of their time) developed into ambitious but also massively tasteless visual gigantism involving flying pigs and marching hammers.

I was there. I watched the wall being built brick by brick. That’s not a Roger Waters lyric – it’s a genuine recollection of a concert. In my early teens I adored Pink Floyd. I collected their most obscure early singles, I lay in my room for hours listening to Wish You Were Here. Punk? What was that? I was fascinated by this strangely intellectual – or was it pseudo-intellectual? – band whose music no living soul has ever tried to dance to.

It all ended when I saw them perform The Wall live at Earls Court in west London. As a huge wall was built in front of the group, I started to feel more alienated than Roger Waters can ever have intended. Surely live music should be more ... live? I went home and sought out some Bowie, Doors and Velvet Underground. Yet somehow Pink Floyd have endured the stigma of their absolute unsexiness and unhipness. They shine on, these crazy diamonds.

I was recently talking to two fellow art critics. We were from three generations. The eldest saw Pink Floyd’s last ever gig with Syd Barrett in the 1960s; I saw The Wall in the Thatcher era; but the youngest turned out to be their keenest fan of all.

It is Pink Floyd’s very lack of conventional style and their distance from youth culture – at least since about 1973 – that is fascinating. They are beyond taste. They may be a bizarre combination of Spinal Tap and Emile Durkheim, but there is something very honest about their odyssey of disillusion. Listening to Wish You Were Here made me dream of being a rock star because anything that promoted this depth of cynical despair had to be a profound experience.

Losing Barrett turned Pink Floyd from dreamy druggy jesters into tragically clear-eyed unpickers of the rock business. “Come in here, dear boy, have a cigar,” as one of the old singles I collected spits. The vaster their success, the more bitterly they denounced the cold and inhuman world they discovered: “And I think I need a Lear jet.”

Only Joy Division ever excelled them in misery. But Pink Floyd are more lucid and eloquent than Joy Division. Comfortably Numb is so monstrously direct it seems obscene – a classic that chills the blood whoever records it. Does Roger Waters’ terrifying vision of modern life come under the category of “art”? Who knows – but it may be the truth, which is a lot more important.

•The Pink Floyd Exhibition: Their Mortal Remains opens at the V&A, London, in May 2017