In Alan Bennett's latest volume of diaries, he quotes Anthony Powell's thesis that "documentaries aren't based on the evidence but are simply scenarios dreamed up by the director, the conclusions known in advance with the facts arranged accordingly." You could say the same about long-established collections belonging to British towns and cities, some of them held since Victorian times. The incumbent curator dreams up the scenario and the objects are arranged accordingly.

Since the opening of the Millennium Gallery in 2001, the narrative woven through Sheffield's permanent collection has been dominated by manufacturing and John Ruskin, with a strong emphasis on celebrating local craftsmanship and technical prowess. The Guardian recently described Sheffield as a city that "never shouts about itself", and often the presentation of the city's collection seems orientated towards boosting local pride, and rightly so. The link between Ruskin and the design work of local makers like David Mellor is a sort of no-nonsense Northern functionalism: art for public good.

While some of these exhibitions feel fresh (the recent Made in Sheffield show demonstrated the production of everything from Yorkshire Crisps and cutlery to local magazine Now Then in playful and inventive ways), at other times the permanent collection comes across a little stale. How many ornithological studies do you need to see in a lifetime? Attempting to inject a little vibrancy into their archive, Museums Sheffield have invited Vlatka Horvat and Tim Etchells to "present a bold, playful reimagining of the city’s historic museum collection", along with a handful of new works. It's an idea with huge potential but most of it has been lost with What Can Be Seen, a show let down by timidity and unrealised ambition.

If the title implies a John Berger-esque examination of curatorship and public exhibition, you'll be disappointed. For the bulk of the one-room show, Horvat and Etchells seem to have merely picked their favourites from the collection's back catalogue and put them on display. These include a collection of pocket watches with and without faces, lantern slides with specimens pressed between plate glass and four strips from a Victorian zoetrope (wouldn't it be more fun to have reproductions actually in a zoetrope?)

The centrepiece of the pair's reimagining is a large rectangular tank stuffed with as many objects as possible, as if it's been lent by the Pitt Rivers Museum. Apparently this creates a “playful dialogue that defies and subverts [the objects’] usual categorisation", in which “historical and contemporary items, biological specimens and geological samples are organised by virtue of physical and material properties such as size, shape and texture creating unexpected juxtapositions, associations and correspondences across very different areas of the collection.” Mostly though, objects of the same shape or colour have been put next to each other and I must have missed the ‘correspondences’ between them. Still, it's nice to see a taxidermied pufferfish in any context, even if it’s been ‘juxtaposed’ with a second world war helmet.

They did manage to dig up one surprising and playful find: a series of aerial photographs taken in March 1962 by specialist company Hunting Surveys Ltd showing the future path of the M1 through England's previously unaltered patchwork of ancient fields and land boundaries. The company used an innovative technique for the time, taking images of the same site from different angles, allowing civil engineers to build a 3D model of the path of the future motorway. The result is a sort of unintentional abstract art, an analog precursor to Google Maps.

Some of the more straight-down-the-line backstage stuff is successful as well. Two of the city's unused statues are presented still encased within the bespoke wooden frames in which they're transported or stored, with foam padding protecting their extremities. It's a clever way of presenting the work: a glimpse under the polyethylene packaging hints that they weren't particularly interesting statues to begin with, and the functional wooden frames unintentionally cut up the forms, deconstructing them and shearing the statue's subjects of their original representations and meaning. One abstract form has a pink plastic bag sellotaped over its face like a murder victim.

The pair are perhaps pointing out that statues – maybe more than any other medium– are liable to be recontextualised, to have their meanings or even their appearances altered beyond the commissioner's original intention. A glowering Queen Victoria used to stand on a plinth outside Sheffield Town Hall but as early as 1930 she was unceremoniously uprooted two miles out of the city centre. Now she sits in a secluded spot in Endcliffe Park, looking pissed off as usual, her imperial pomp dampened by bird shit, graffiti and overhanging chestnut trees.

Another high point is a series of new photographs in which Horvat and Etchells document the haphazard and piecemeal cataloguing system used within the organisation. In the classic tradition of top-down public sector reorganisations, it appears that the entire collection has been re-catalogued every couple of years since the 1870s, leading to many items being lost, mislabelled or simply designated as unknowns. A handful of photos capture a snapshot of the anarchy, with boxes labelled “useless destroyed” and “Emperor's wives, daughters, sisters etc. 57bc - 138ad” (the best being a photo of a drawer simply labelled “Dark age, etc.”)

What Can Be Seen isn’t a bad show, just one that could have much more to say. The title’s similarity to Berger’s 1972 series ‘Ways of Seeing’ led me to hope it might take a more political angle, especially with it focusing on the Socialist Republic of South Yorkshire. There’s questions to be asked about how these vast permanent collections come into being. When a local captain of industry like Sheffield’s J.G. Graves bequeaths his treasure trove to the city, is that an apolitical act? How do the values and political affiliations of men like Graves, who kick-started collections across the country, influence how those works are presented and viewed decades after their death?

In a video accompanying the show Horvat states that the phrase ‘what can be seen’ also begs the question of what cannot be seen. The creation and the curatorship of art, what is included and what is left out, is intrinsically linked to the history of wealth and to changing social attitudes towards the rich and their gewgaws. What’s needed now is for Horvat and Etchell’s idea to be developed further. A more ambitious show would see the coded meanings and political undercurrents running through the century-old collection exposed and subverted by new work linked with the old. If these objects – 1920s knuckle dusters, 50s record racks, stuffed birds and ornate pocket watches – were interrogated, their original purpose questioned, they might tell us something new about what we value, about an alternative history of Sheffield, about the purpose of art and design.

Tim Etchells and Vlatka Horvat, What Can Be Seen, is at Sheffield Millennium Gallery until 7 May