By James Westcott

Now that Boris – his opponents in London's mayoral campaign tried desperately not to label him only by his cute first name, but allow the slip – is settling into city hall, London and its artworld in particular awaits an announcement on what he'll do with the fourth plinth in Trafalgar Square, which currently hosts Thomas Schutte's Model for a Hotel (2007) and has since 1999 been a forum for a series of commissioned artworks. In his campaign for mayor, Johnson, a former Conservative MP, threw his considerable weight behind the proposal to ditch contemporary art on the plinth and replace it with a statue of Sir Keith Park, commander of the RAF squadron responsible for defending London and the south east during the Battle of Britain.

The elite of London's artworld, including Nicholas Serota of the Tate, Whitechapel director Iwona Blazwick, James Lingwood of ArtAngel, White Cube's Jay Jopling and Julia Peyton Jones of the Serpentine, co-signed a letter to the Guardian in March protesting Johnson's plans, arguing that 'The series of commissions on the plinth presents 21st-century London as a forward-looking, dynamic and progressive city with a rich heritage.' To choose any one statue – or indeed artwork – to sit permanently on the fourth plinth would 'limit rather than extend the impact of public art in the city'.

Shortly before the election, Guardian columnist Lynn Barber was rather more blunt, and in fact incorrect, when she wrote: "Yet another reason for hoping Boris Johnson does not become mayor of London is that he has pledged to dump the fourth plinth competition and put a Spitfire on it instead.' There'll be no Spitfire at any time, but it would be particularly brutal of Boris if he abandoned the competition already set in motion last year for the next artwork on the fourth plinth. James Lingwood, a former member of the Fourth Plinth Commissioning Group, told artreview.com: "When the mayor's office has made a commitment to a certain process it would be nice to think that the incoming mayor would honor those commitments and take a bit longer to debate and consider the longer term future of the plinth.

"Were they to put up a sculpture of a World War II hero, I don't think there should be a presumption that it would be permanent anyway", says Lingwood. "I think if Boris wanted to put it up for the duration of his incumbency there's very little to stop that. But the assumption that a decision made now would imply permanence is questionable." Lingwood remembers how, around 1996 and 97 when debate about the fourth plinth was beginning, one of the most popular figures the public wanted to see on the plinth was Paul Gascoigne.

Among the six proposals on the table, with a winner due to be announced imminently – and now perhaps uselessly – Tracey Emin had suggested a family of little meer cats peering off the plinth, Antony Gormley had wanted to make a public stage of the plinth that anyone can use, Jeremy Deller intended to put a bombed-out car from Iraq up there (deliberately 'not an artwork', he said), and Bob and Roberta Smith designed a shaky-looking tower with a wind turbine, solar panels and a peace sign, to be called Faites l'Art, Pas la Guerre. Now instead we could be faced with another statue about war. Or perhaps Johnson will get a bit more serious now he's in office and realise that removing a piece of art and replacing it with a war hero doesn't really chime with the socially tuned-in modern image the Conservatives want to project. He should at least give a stay of execution to art on the plinth and install the winner of the current competition for its full tenure before lowering Sir Keith Park into position.

It's been a while since contemporary art received a serious public knock-back like Johnson's. Since the YBAs shocked and then inured the media to being shocked by contemporary art, the trend has been more towards happy acceptance, baffled curiosity, a jolly-good-sport willingness on the part of the press and the public to be entertained by this stuff. The Turner Prize, the Turbine Hall, the Angel of the North, Banksy, Damien Hirst's skull and the Frieze art fair have all become a fluent part of the media vocabulary and monuments themselves in Britain's cultural landscape. All of which is to say that even as contemporary art is more popular than ever, it may not be really taken seriously – or, worse, isn't taking itself seriously as a critical (or indeed propositional) way of looking at the world. If contemporary art gets so easily accepted, we should all be more worried than we are.

As sad as it would be to lose the important delight of an unexpected encounter with art in Trafalgar Square, it could be an exhilarating shot in the arm for the economically supercharged but existentially listless artworld to come up against some good old fashioned resistance and rejection for a change, something akin to the cutting of the National Endowment for the Arts grants in the US in the 1980s and 90s, which enraged and impoverished a generation of artists, but also perversely confirmed that what they were doing was considered of (subversive) consequence, if the government wasn't willing to support it any more. (The recent cuts in Arts Council funding hit performing arts much harder than visual art, and didn't come with the same politics as the culture war over the NEA.) Going further back, the Federal Art Project in the US during the depression saved artists from the breadline and affirmed their civic if not commercial importance, but it was only after the Project was gradually cut and ultimately withdrawn in the 1940s that American painting became articulate enough to shove Paris aside and swagger to the very tip of the avant garde.

Now – at least from this side of the artworld – it seems that no public institution, politician, property developer or philanthropist wants to risk being on the wrong side of history when it comes to art, so everything gets facilitated, encouraged, accepted and instrumentalised. In the early development of the fourth plinth concept, the many interested parties could not agree on what art would accrue historical and public significance, so instead a virtue was made of the uncertainty and everything got a rotation, a hearing, column inches – but in the process it risked being seen as a gimmick or a game by cultural conservatives like Johnson. As retrograde as his plans are, one shred of solace we might take is that at least Johnson is risking being wrong (not only risking, in fact, but succeeding), and in doing so reaffirming the crucial potential for art to be widely misunderstood and rejected.