Jeff Koons plays the Ashmolean Museum. The junk-bond superstar brings his exorbitant bling to the world’s oldest public gallery, supersized baubles among the urns and sarcophagi. It’s a talking shop (£12.25 a head) at the very least. Here they stand, rows of colossal objects cast in mirror-bright steel – bunnies and ballerinas, piglets and balloons, in silver and gold and eye-popping magenta, their polished surfaces giving us nothing in return but our own mugs. The fun-house reflections are enough to baffle the eye – but what about the mind?

Koons has always been as vacuous as he wants to be. Time has changed nothing except his ramping prices. This show is being sold as a condensed survey of the artist’s work from the 1980s to the present day, with examples of his various product lines – Statuary, Banality, Antiquity and so on, right up to the recent Gazing Ball works, in which shiny spheres are attached like footballs to copies of famous paintings and sculptures.

Certain series have been sidestepped, notably Made in Heaven, which may have something to do with the anal sex and general pornographic boastfulness of Koons’s photographic self-portraits. And who now wants to show the porcelain statue of Michael Jackson and Bubbles, in which the singer appears in white-face with his pet chimp?

But even allowing for these omissions, it seems significant that such a prolific 40-year career – Koons was born in Pennsylvania in 1955 – could indeed be represented with only 17 works.

The show opens with superb drama. Hanging before you, like an exclamation mark in mid-air, is the ebullient orange sphere of a Spalding basketball suspended in a vitrine of water. Its position – neither sinking nor rising but in perfect equilibrium – was so complex to achieve that it required the involvement of the Nobel physicist Richard Feynman. The sight is so abrupt as to be a never-ending surprise each time you circle back to it – a feat in itself, and a sensation somewhere between delight and laughter.

Koons made this ice-breaker of a work in 1985. The original idea was there, long before Damien Hirst suspended his shark in a tank. Changing course the following year, Koons came up with the even more famous Rabbit. And here it is, this deathless bunny cast in silver steel, an innocent balloon sculpture transformed into something more like a voodoo doll, nightmarish and yet inane.

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Soft but hard, cute yet steely, light as a balloon and yet heavy as metal: those are the basic oppositions. Rabbit is fully counterintuitive. And that’s the way it has gone these many years. The enormous Seated Ballerina in this show, completed in 2015, sits in a froth of blue tutu, bending down to tie the delicate ribbons of her ballet shoes, which look like nothing so much as drawings from the bright frame of some Disney cartoon. You are to marvel at this remarkable effect – so dainty, so transparent and ephemeral – while noticing that it is somehow achieved with a hundredweight of cast steel.

Koons, ever the most ardent proponent of his own work, says in the catalogue that he aimed to make a work that absolutely anyone would like. And who could resist the beauty of Gazing Ball, a mirror-bright sphere cast in cobalt blue steel, so flawless, so glassy, so unimpeachably perfect? Koons balances one on top of a shell-shaped classical fountain – the pearl in the oyster – and another on the shoulders of the most reproduced classical sculpture in history, the mighty Belvedere Torso, which inspired Michelangelo. It looks like a party trick – the footballer shouldering the ball. A neat joke; but what else?

One thing about this compact show – and Koons’s whole aesthetic – is that it puts everything on exactly the same level as anything else: the classical sculpture and the Disney ballerina, the basketball, the pig and the baby Jesus. Nothing is greater or lesser or more significant: not the smart new Hoover or the martyred saint. And the works in this show, we are told, put past and present on equal footing. Look at the Belvedere Torso, Koons argues, and you are both together in the here and now.

Koons has curated the show himself, along with Norman Rosenthal, late of the Royal Academy (can it really have taken two brains?). The works are arranged so that you come upon the most monumental work, without knowing it, from behind. It seems at first to be another gigantic balloon sculpture, roughly the colour of a ruptured appendix and with overtones of dangling scrotum besides. But come round to the front and you discover that it is in fact a female figure: the Venus of Willendorf, with hints of the Statue of Liberty’s diadem – three different eras in one. Except that even this revelation feels over-inflated. For what draws the viewer isn’t the way Koons aims to imitate an ancient goddess in cheap party balloons, but the hyperbolic brilliance of the surface – brighter than anything in nature, as it seems – and then the feat of repeating the whole thing in steel. Whereupon you catch yourself gazing into that empty surface, along with everyone else.

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Jeff Koons’s sincerity, it seems to me, is not in doubt. His Banality series – to which the pig belongs – was never more candidly named. The quartet of mediocre paintings in this exhibition, montaging classical figures with modern landscapes and scribbly drawings, are just as trivial as they sound. Yet Koons revels in their silly sight gags, repeating them in different colour-ways. And why not, he seems to shrug? Why argue with the pleasures of spotless reflections, magic balls, gigantic dolls, especially if the formula works, wouldn’t it be like resisting the simple toys of childhood?

Except, of course, that the works are manufactured with such determined precision. Not the basketball, which depends upon the most exacting of physics; but the sheen on the ballerina, which mimics colour seen through colour, like the overprinting on a china figurine; or the terrible dead surfaces of the canvases, that speak painting by numbers. This is calculated nostalgia; just as the big blue spheres resemble nothing so much as outsize Christmas decorations, in which you see the world made pretty, harmless and small.

This is an art to deflect thought, and ultimately even viewing. Look at it for too long and you sense its sterility. Koons’s pitches for his work, which appear on wall texts throughout, are amiably generous and inclusive – but they never aim higher than platitude. And so it is with the objects themselves. Stare at their polished perfection and all you see is the shining fatuity of it all.

• Jeff Koons is at the Ashmolean Museum, Oxford, until 9 June

Jeff Koons: hits and misses

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1986 Rabbit becomes Koons’s most famous steel inflatable, its popularity rivalled only by Puppy, the gigantic, flower-covered terrier outside the Guggenheim in Bilbao. Editions of Rabbit proliferate, one soft version rising to 50 feet.

1989 The Made in Heaven series – kitsch sculptures, photographs and paintings featuring explicit sex acts with Koons’s then wife, the porn star and libertarian politician Ilona Staller – causes outrage at New York’s Whitney Museum. Koons reportedly destroys some of the works following their divorce. Critics hate the series, but notoriety helps boost Koons’s auction prices.

1996 The Celebration series – giant love hearts, building blocks, Easter eggs and balloon dogs cast in steel – is due to be shown at the Guggenheim in New York. The works are said to herald the longed-for return of Koons’s young son with Staller. But production problems and mounting costs derail the exhibition. It will be another decade before the sculptures are shown at the city’s Metropolitan Museum.

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2013 Balloon Dog (Orange) sells for $58.4m at auction, the highest price ever paid for a sculpture by a living artist. Koons describes it as “materialism and monumentality”. There are four more editions, one – in shocking pink – shown to some controversy at Versailles.

2018 A huge, hyperreal hand clutching a bunch of multicoloured balloon-sculpture tulips is given by Koons to the people of Paris in memory of the victims of the 2015 terrorist attacks. Attempts are made to stop it being installed by the Palais de Tokyo. Parisians are not impressed by the work’s brashness and apparent insensitivity. Artists including Christian Boltanski protest in an open letter to Libération. Koons wins out in the end. LC