Prize-shortlisted poet Ralf Webb begins his compact study of same-sex desire in four 20th-century American authors with Tennessee Williams, who said he couldn’t write a play without a character he lusted after. In A Streetcar Named Desire (1947), he wrote one everyone else fell for, too, in the shape of antihero Stanley Kowalski – for the writer Gore Vidal, a sharp turn from the traditional dashing male lead to a “sexed” one, at least as embodied by a cap-sleeved Marlon Brando. A month after its first performance, Alfred Kinsey published Sexual Behaviour in the Human Male: 800 pages of incendiary testimony from anonymised interviewees to the commonplace nature of gay desire at a time when the US army stigmatised it as a perversion weakening national might.

A growing contemporary interest in Freud, together with panic about communist subversives, added to the volatile swirl shaping ideas of sex at the time Strange Relations’s other central case studies – Carson McCullers, John Cheever and James Baldwin – lived and worked. Webb’s approach, more silky synthesis than scholarly spadework, mixes lecture-hall lit crit with the style of a jet-set spy thriller: “January 1889, Camden, New Jersey.” So begins an opening chapter on how Walt Whitman’s Leaves of Grass laid the ground for how American writers might conceive of gay desire in the coming century: “In the dimly lit living room of a modest, two-storey timber-framed house, an enormous grey-bearded man lolls on his rocking chair, a wolfskin draped over the back. Dusk falls… he is ill. Seriously ill. This is the American poet Walt Whitman, at 69.”

While it’s hard not to read this kind of thing without cringing just a little, it does effectively plunge you into the moment; the literary criticism, by contrast, is sometimes written in such a way that forces you to read and reread in search of a foothold on Webb’s meaning. Look at what he says here about Whitman’s Children of Adam poems: “the gender ambiguities, dream logic and untethered ‘I’ raise the possibility that – beneath the excessive cladding of all the procreative, phallocentric imagery – there is a different, even more democratic, erotics at play in this cluster of poems: a lambent sexuality in which gender is liberated from a binary position, becoming an object of free play”.

Webb, yo-yoing between both modes, is always more convincing when he remembers to let us come up for air. He’s clear-eyed about the pros and cons of describing his chosen writers as “bisexual” and “queer”, justifying his doing so as a way to catch how desire is “changeable” as “quicksilver”. But while he’s vigilant for dubious moments in their work – narrowing his eyes at, say, Whitman’s interest in eugenics and bodily perfection – he’s keener to highlight ways in which hierarchical thinking is critiqued (a go-to word). As a guide, he’s even-handed and sensitive, yet sometimes you crave a bit more friction, a little more spunk: his analysis can seem oddly ethereal, given the private turmoil and public danger that sex could entail for the authors under discussion, not least Baldwin, cornered by the weight of racist assumptions, whether he’s being groped by a white man while on a magazine assignment in the south, or slapped by his white girlfriend in a New York street.

The chapter on Cheever is by far the best, probably because his tormented private life and slyly off-kilter fiction best suit the book’s procedures. For one thing, we forget the slightly hammy nature of Webb’s more novelistic mode when he’s bringing us, for instance, Cheever’s morning routine of taking the lift, freshly suited among other office workers in his block, only to descend to the basement and strip to his undershorts to hammer out his latest New Yorker tale. Or take the moment when he’s at a Broadway performance of Streetcar, watching Jessica Tandy play Blanche as she discovers her husband’s desire for another man – all the while nursing his own private desires, sitting beside his wife, pregnant with their second child.

But it’s also that there’s an evergreen tang to the way Cheever approached writing fiction as a desperate husband in gin-pickled suburbia – see his story The Enormous Radio (1947), about a couple ruined by fomo when their fancy new wireless broadcasts their neighbours’ private lives. His not-quite-realist output lends itself to livelier summary than sexual dynamics in Williams or the fiction of McCullers, whose 1940 southern gothic The Heart Is a Lonely Hunter – unrequited love, madness, suicide – Webb strenuously rescues from criticism that it retreads “archetypal gay tragedy”.

There’s some overlap here with Olivia Laing’s 2013 study of alcoholic writers The Trip to Echo Spring (a title taken from a line by the antihero of Cat on a Hot Tin Roof). Laing likewise jazzed up lit crit with novelistic biography, but there was also an element of memoir, too, an unashamed I-ness that Webb could do with, simply to quell the faint muttering: why these writers, why him, why now? Telling us they’re a balm for “our contemporary crisis in masculinity” feels merely like a place for the book to hang its hat. Ultimately, I wondered if, for Webb, the period’s allure lies not just in its ferment of ideas, but in the clout contemporary literature enjoyed as a means with which to address them: a time-limited era in which a novelist such as Baldwin could run rings around his interlocutors on live television, a stage play could transform our view of masculinity and a book of poems “left an indelible impact on the entire culture”. Maybe, but if there’s a hint of elegy here, perhaps there’s expedience, too, given that the period at hand is plenty nourishing enough to get by without a thesis.