In the main hall of the Imperial War Museum, London, the outline of a drone has been marked out in white lines by the artist James Bridle. Yet this ghostly image of 21st-century war immediately exposes the intellectual weakness of the exhibition it announces.

Do we really live in an age of terror? Looking around I am not convinced. Towering above the drone drawing is the museum’s most frightening and stupendous “treasure”: a V2 rocket. Next to that is a V1 flying bomb. Compared with the first half of the 20th century, when two world wars ravaged humanity, ours is still – for all its fears and troubles – comparatively fortunate.

Perhaps that lack of fit between anxiety and reality accounts for the dubious relevance and patchy, roped-in feel of much art in this exhibition. Age of Terror makes grand claims about contemporary history that it fails to prove. The fact that Grayson Perry went into his studio the day after 11 September 2001 and added cartoon planes to the pot he was working on tells us nothing about terrorism. Just as silly is a work by the Chapman brothers called Nein! Eleven which portrays the Twin Towers as dual mounds of tiny dead Nazis. Yet these glib artworks tell us something after all: that for many people, probably most of us, terrorism is marginal. The idea touted here, that it shapes this century’s art, is ludicrously melodramatic and morbid.

Grayson Perry’s Dolls at Dungeness, September 11th 2001. Photograph: Stephen Brayne/Victoria Miro Gallery

No doubt it’s the last thing the curators intend, but their vision of our time is oddly similar to Donald Trump’s. For Trump, every crime is related to Islamist terrorism and that menace justifies the destruction of democracy itself. Coming from a political polar opposite, this exhibition insists that contemporary art is shaped by the shadow of 9/11 and the consequent war on terror.

Age of Terror might be better if it got its recent history right. For instance, there are works here about the war in Syria, including Julie Mehretu’s eerie abstract drawing of a dying city entitled Epigraph, Damascus, and a film about children in wartime by Syrian artist Khaled Abdulwahed. Yet why does this exhibition present Syria’s tragedy as a chapter in the war on terror, putting these alongside works about Iraq and Afghanistan? Surely Syria’s war started when protests against Bashar al-Assad’s dictatorship were met with state violence: it grew out of the Arab spring, not western intervention. Or have I not been reading the right conspiracy websites?

A survey of artistic responses to 21st-century conflict is definitely taking on more than it can handle. Yet the powerful introduction to the exhibition reveals why it is so hard to avoid thinking of these strange times of ours in terms of terrorism. The truth is that we just can’t get 9/11 out of our minds.

Rachel Howard’s Study (2005). Photograph: Prudence Cumming Associates

Manhattan resident Tony Oursler saw it from up close. This powerful artist had a terrifyingly intimate view of the catastrophe and used his skills as a video artist to make his own spontaneous documentary. Oursler’s film 9/11 is a street-level view of the tragedy that makes you relive the cruelty and chaos of that day with terrible intimacy. He watches a body falling, exclaims on the soundtrack as the first tower falls, meets a woman waiting for news of her workmates in the Windows on the World restaurant.

Ai Weiwei’s Surveillance Camera With Plinth (2015). Photograph: Adam Reich/Lisson Gallery

Hans-Peter Feldmann collected the next day’s newspaper front pages from all over the world. His display makes the terrible impact of this act of terror disturbingly immediate. “A declaration of war,” said the Guardian over a full-page image of the burning towers.

9/11 provoked the best art here, which includes Indrė Šerpytytė’s apparently abstract painting of metallic vertical lines. It is chilling to realise they represent the facade of one of the towers as seen by someone who jumped and plummeted past this classic of modern architecture at an estimated 150 miles per hour.

It is a lot harder to be troubled by Jitish Kallat’s sculpture of people being frisked at airport security, in the section of the exhibition called State Control. Poor us, we have to endure tighter checks at airports now. Annoying, but compare it with the real terrors of the last century that fill this museum. A surveillance camera is not a V2, even when Ai Weiwei renders it in marble.