What are the life skills appropriate to an artist’s muse? Hotness is a given; and sexual availability, while not compulsory, has generally been appreciated. The ability to keep a house tidy is a plus, as is being supportive of the artist at all times, even if he – and it is nearly always he – is being an arsehole. It helps, of course, to be mysterious; if one is to be endlessly gazed at, it’s best not to give everything away at once. As for a life, and a career of one’s own, well, history has shown that such things are rarely tolerated.

In Marianne & Leonard: Words of Love, out later this week, the filmmaker Nick Broomfield examines the on-off relationship between the late Marianne Ihlen, a Norwegian single mother, and the poet and musician Leonard Cohen, whom she met on the Greek island of Hydra and who died just four months after her in 2016. Ihlen was immortalised in the song So Long, Marianne, and inspired Cohen to write Bird on a Wire. Since Ihlen gets first billing in the title, one might assume that this is her story, a biopic of sorts, but instead it depicts her through the prism of the men in her life. These include the novelist Axel Jensen, who left her not long after their son, Axel Jr, was born; Cohen, the towering genius whom we are told she could never hope to tame; and Broomfield himself, who had a fling with her during a visit to Hydra in his early twenties.

While a drug-addled Leonard bashes out the novel Beautiful Losers on his typewriter, she lovingly brings him sandwiches

In the voiceover, Ihlen’s recollections of life with Cohen include doing the shopping and preparing meals. While he, drug-addled, bashes out the novel Beautiful Losers on his typewriter (later described as “verbal masturbation” by a Canadian critic), she lovingly brings him sandwiches. Sometimes, she says, she simply sits at his feet. Marianne & Leonard is undoubtedly handsome and atmospheric, much of it made up of grainy footage of the couple and their friends, and shows Hydra to be little more than a mirage, a place where children are neglected and couples fall apart. But perhaps the film’s most enduring message is what a massive ball-ache it is to be a muse.

It’s easy to scoff now, of course. We live in a time when women are seen as capable of making great art, even if the old structures ensure they don’t always get the chance. Still, the history of art, music and literature is littered with women upon whom muse status has been bestowed but whose lives appeared to be miserable and whose legacies remain indistinct. Consider the pre-Raphaelite “stunners”, immortalised in oils by Millais, Rossetti, Holman Hunt and friends, as medieval queens and ancient goddesses. Nice work if you can get it, except that poor Lizzie Siddal nearly caught her death posing as the drowned Ophelia in the bath, and Jane Burden, muse to William Morris and Rossetti, is better known for her abundant hair and pouty lips than her embroidery, which was integral to the Arts and Crafts movement.

‘In her lifetime, the painter Frida Kahlo’s work was overlooked in favour of her artist husband, Diego Rivera.’ Rivera and Kahlo circa 1945. Photograph: Hulton Archive/Getty Images

Not all artists make their muses lie in freezing baths, but they’re not above eclipsing their careers. Ask Marianne Faithfull, who was a singer before she met Mick Jagger, though as his girlfriend became, in the immortal words of the Rolling Stones manager Andrew Loog Oldham, “an angel with big tits”. No wonder her masterpiece, Broken English, didn’t emerge until after she and Mick had split. In her lifetime, the painter Frida Kahlo’s work was overlooked in favour of her artist husband, Diego Rivera, who loved nothing more than to paint his wife; only in death did she finally get the credit due to her. Camille Claudel was an artist in her own right but barely got a look-in during her relationship with the sculptor Auguste Rodin, and ended up destroying much of her work. The list of women overlooked, cast aside or actively ruined by their artist lovers goes on.

Present-day muses seem to fare better: you’d scarcely find a man in the fashion world who wouldn’t claim Kate Moss as his muse, but she is nobody’s subordinate. Karl Lagerfeld had scores of muses, among them Kristen Stewart and Cara Delevingne, though both appear to be in the driving seats of their careers. Do women artists have muses? Probably, but they’re far less likely to make a show of it, or expect the focus of their gaze to ply them with sex and sandwiches.

Judging by his film, Broomfield is enamoured with the idea. Marianne & Leonard prostrates itself at the feet of Ihlen’s beauty and celebrates her nurturing spirit but doesn’t seem interested in her inner life, or indeed her suffering. Why? Perhaps because to delve deeper risks puncturing the otherworldliness and genius of male artistic endeavour, and that just wouldn’t do.

• Fiona Sturges is an arts writer