In a gallery at PS1, the experimental affiliate of the Museum of Modern Art in New York, a scribbled note pinned to the wall reads, "Michael Landy did it better . . . "

Bob and Roberta Smith, also known as Patrick Brill, the artist who made such a brilliant splash at Kilkenny Arts Festival and the Butler Gallery in 2013, has come up with Art Amnesty, an invitation to anyone to put anything they like on the walls. They can even knock up something on site – pencils and paper are provided. The only condition is that at the end of the show it must be destroyed.

Meanwhile, over in Japan in August this year, Landy put an enormous transparent skip into Yokohama Museum of Art and likewise invited artists to consign their works to destruction. Art Bin is a remake of an earlier Landy project, in 2010, at the South London Gallery, where Damien Hirst – never one to pass up a potential headline – chucked a print of his diamond-encrusted skull, For the Love of God, into the mix.

An atmosphere of fun surrounded both shows, but it caused me to wonder: what if those artists were doing it with books? Imagine a library inviting people to bring along books on condition that they were burned? Add to that the thought that there’s nothing particularly unique about a book (unless it’s a single surviving copy – a Book of Kells, for example), and it’s a short step to the sneaking suspicion that, despite protestations, we harbour a deep loathing of art.

Except that’s not quite it.

Looking at Art Amnesty, which runs until March 8th, 2015, is uncomfortable. A sense of anxiety emerges. With all the disparate works, tacked up on the walls, it's impossible to know what's "proper" art. It is stripped of all the value-making apparatus of the art world: careful placement, lots of white space, reverential and often impenetrable expert texts, and a consensus of adoration from the coterie keen to pick up their next freelance curating gig.

It’s like seeing the expensive T-shirt you shouldn’t have splashed out on at Brown Thomas screwed up on the floor in the discount corner of TK Maxx. Is it still desirable? Does it hold its value?

Smith’s show is deliberately patchy and scratchy, and is a reminder of all the things that attach themselves to art that have little to do with the work. It exposes the cracks in the process by which the art world rarefies its objects and products, so that a scribble can be valued at millions. It’s a process of celebritisation, an elevation of someone or something way beyond the sum of its parts.

An artist who thrives on provocation, Smith says his current project is him “trying to get us to think about art with its clear psychological value outside the market; trying to wrest a bit of art away from the huge collectors and the idea that [arts] philanthropy will solve everyone’s problems”.

It did something else to me: it made me realise just how much bad art is out there, art that nevertheless gets framed by the art-world consensus of acceptance.

Obviously, art, like anything, is subjective. You don't have to like it all, and some of the most interesting conversations about it can start from disagreements. But increasingly I find it just doesn't always add up in the gallery. In a recent review of the current Turner Prize exhibition, the Sunday Times critic Waldemar Januszczak asked: "When did art decide we owe it this much unearned attention?" Of one of the nominees, Duncan Campbell, whose work is also on show at the Irish Museum of Modern Art, in Dublin, Januszczak observed: "Being lectured to for 54 minutes by someone as self-indulgently uninterested in encompassment as this is a torture of medieval intensity. That said – and this will really shock you – Campbell is probably the best artist here . . . "

If Campbell wins the Turner Prize, his career will be assured. It has become the ultimate imprimatur of an art world that seems to want to agree among its limited selves on the value of its darlings rather than encourage active and healthy debate about what is working and what isn’t. This situation is unhelpful to the good art that’s struggling for attention.

Sometimes the best critiques come from outside, such as when, in 1993, Bill Drummond and Jimmy Cauty, who together made up the K Foundation, offered €40,000 (then exactly double the Turner money) to the "worst artist of the year", inviting the public to vote on the same shortlist as the Turner Prize itself. The Irish-born artist Sean Scully was on the list that year, but Rachel Whiteread famously won both the Turner and the worst-artist award.

She refused to accept until lighter fluid and a flame were produced. Whiteread took the cash and donated it to charity. The following year Drummond and Cauty went ahead and burned £1 million, making a house brick from the ashes. Was this a vile waste of money when people are in need? Not so much as the $81.9 million someone spent this month on Andy Warhol's Triple Elvis at Christie's in New York. Something for the Art Bin, perhaps? As someone who loves art, I'd be very tempted.