So the Saatchi Gallery is to be renamed the Museum of Contemporary Art, London. The Saatchi Gallery will now join museums of contemporary art in Sydney, Los Angeles, New York (where the museum of contemporary art is better known as the New Museum) and various other major and not so major cities. What hubris, I thought, when I first heard the news. On reflection, this seems churlish. It is an extremely generous gift, and the building itself is a great space for art, is extremely popular and attracts a very broad audience. But it is the collection that is likely to be problematic.

Exhibitions at the Saatchi Gallery are invariably incoherent: the work he shows can be spectacular, but alongside the good there is plenty that is bad or mediocre. We don’t even know what art Saatchi currently owns, or what he is giving to the nation. Even the works he is giving are variable in quality, and not always even the best works Saatchi first exhibited. There’s no artist’s film and video, for instance, and little good photography – and how can you have a museum of contemporary art that ignores these media?

For all his money and enthusiasm, Saatchi has never bought consistently or well. What else is Saatchi donating? Not more Ron Mueck, please.

Unlike other collections of contemporary art that have been shown internationally – the collection of Belgians Anton and Annick Herbert, or the collection of the legendary late German gallerist Konrad Fischer, both of which were built up over decades – Saatchi’s collecting has never had any focus. Young Brits have come and gone, as have artists from the US, Germany, India, China and the Middle East.

Whatever happened to the New Neurotic Realism, an entirely made-up movement that never went anywhere? Richard Wilson’s lake of reflective oil, Tracey Emin’s bed and Jake and Dinos Chapman’s sexualised mannequins never seemed to have much connection, except that they were made by British artists who live in London and happen to know each other. Put these works together with some of the others mentioned and one can only imagine a series of nightmarish, specious exhibitions that misrepresent the trajectories of contemporary art. The hope that the collection will evolve must be tempered by other questions, too: who will curate? What will be bought, and what sold off? Most of all, what does it mean to “continue the same policy that was established when the gallery began 25 years ago”, as the press release has it? The truth is that there never was any policy. In the end, there is only Charles Saatchi: his enthusiasms and, now, his generosity.