In his influential book The Empty Space the English director Peter Brook wrote about what he called the Holy Theatre, or "the notion that the stage is a place where the invisible can appear". He lamented its death in the European theatre and looked towards its revival.

Brook drew on three figures as totems of inspiration: the French actor and writer Antonin Artaud, the American dancer and choreographer Merce Cunningham and the Irish playwright Samuel Beckett. He did not mention WB Yeats at all, even though he was describing exactly what Yeats had wanted to do in the theatre. Here is one token of the way Yeats the dramatist had not so much fallen out of fashion as never quite become fashionable in the first place. The holy theatre Brook was invoking was certainly what Yeats also longed for. But Yeats's plays have always struggled to hold their place against the monumental presence of his poems.

In a sense the most damning verdict on Yeats's lifelong engagement with the theatre comes in the prologue of his own last play, The Death of Cuchulain, in which the supposed producer appears as a mad old crank, making a virtue of the necessity of playing to a small and select audience: "I wanted an audience of fifty or a hundred, and if there are more, I beg them not to shuffle their feet or talk when the actors are speaking . . . If there are more than a hundred I won't be able to escape people who are educating themselves out of the Book Societies and the like . . . pickpockets and opinionated bitches."

That contempt for an ordinary audience – and the protesting-too-much desire for a pitifully small house – is self-parody, but it acknowledges the failure of Yeats's drama to embrace the essential vulgarity of the theatre. As Yeats's friend John Synge predicted, "I do not believe in the possibility of 'a purely fantastic, unmodern, ideal, breezy, spring-dayish, Cuchulainoid National Theatre' . . . No drama can grow out of anything other than the fundamental realities of life, which are never fantastic, are neither modern nor unmodern and, as I see them, rarely spring-dayish, or breezy or Cuchulanoid."

That failure has to be set against Yeats’s once high ambitions for the theatre. As a founding member of the Irish Literary Theatre, in 1899, and later as dramatist, codirector, manager and propagandist for the Irish National Theatre Society – better known after 1904 as the Abbey Theatre – Yeats threw his immense energies into the making of plays. He did so because he believed that a supposedly ancient form of tragic verse drama would play a leading, even decisive role in reinventing an Irish national culture.

Yet, by 1937, looking back, he admitted that this tragic drama had never taken fire in the public imagination: "My audience was for comedy – for Synge, Lady Gregory, for O'Casey – not for me. I was content, for I knew that comedy was the modern art."

The vision he once had of the Abbey as a kind of Irish Bayreuth, with himself as the Irish Wagner, fusing ancient myths into a total theatre, was long gone. As early as 1916 he had taken refuge in the notion of an elitist drama: “I have invented a form of drama, distinguished, indirect, and symbolic, and having no need of mob or Press to pay its way – an aristocratic form.”

The great puncturer of that artistocratic pretension was Yeats's successor, Samuel Beckett. It might be telling to mark the gulf between William Butler Yeats and Beckett, whose influence on 20th-century theatre is unquestioned. Beckett remarked in 1980 that Yeats "went after all the wrong things in Irish life"; for him the poet's brother, Jack B Yeats, was a much more productive influence. When, in Beckett's early novel Murphy, the anti-hero decrees in his will that his ashes be flushed down the lavatory at the Abbey, "if possible during the performance of a play", Yeats's theatrical legacy is given the middle finger.

Yeats was overwhelmingly interested in symbolism, Beckett overwhelmingly insistent on not being symbolic. Yeats drew for most of his theatre on the heroic world of Irish mythology, Beckett on tramps, vagabonds and derelicts. There is a grandiosity to Yeats’s plays that Beckett chased (and laughed) off the stage.

Yet things are not so simple. Beckett did see Yeats's plays at the Abbey, and their impact is obvious: the compression, the starkness, the belief that a dramatist must write not mere words but whole actions, the use of repetition, the sense of the stage not as a slice of life but as a supercharged ritual space. In the second act of Beckett's Happy Days Winnie says, "I call to the eye of the mind . . .", half-remembering the line from Yeats's play At the Hawk's Well. The quote is not accidental: Beckett, like Yeats, asks us to see with the mind's eye. And it is surely impossible to encounter the stark setting of Yeats's Purgatory – a road, a tree – without thinking of Waiting for Godot. That play, in turn, could be an enactment of Yeats's thought in an early draft of At the Hawk's Well:

Accursed the life of man. Between passion and
Emptiness what he longs for never comes. All
his days are a preparation for what never comes.

And while Yeats at one point suggested putting actors in barrels on castors that could be pushed on and off stage with sticks, Beckett has the protagonist of Endgame in a chair on castors – and his parents not quite in barrels but in dustbins. Maybe there is some continuity between Yeats and Beckett after all.

Perhaps the real problem with Yeats the dramatist is that he asked to be judged by two successive, and equally preposterous, standards. The first was that his drama should vivify an entire nation; unsurprisingly, it didn’t. The fallback position was that it should appeal only to a socially superior and impossibly refined audience; even if it did, there is something obnoxious in the ambition. But what if we scrap both of these standards and adopt a plain and ordinary one: are these plays any good? Can they hold the stage and touch something in an audience that approaches them with an open mind?

If we take away the ideological trappings of an aristocratic theatre and contempt for the mob, Yeats’s failure to realise his great project of a tragic national drama does not look so ridiculous. His drama is a body of work that, if he had never published a poem, would still make him a remarkable figure.

Although some may feel it's not saying much, he is easily the most successful writer of poetic drama of the 20th century. He is restlessly inventive, moving between the extreme formality of his Noh plays and the almost-naturalism of a late play like The Words Upon the Window-Pane, moving between verse and prose, masks and faces, between ancient myths and modern moments, stripping the stage of its naturalistic clutter and seeking to integrate music, dance, light and a severe visual presence into contemporary drama.

If anything these innovations work against his reputation. Yeats is too often left to amateurs, but he is rigorous and relentless in the demands he makes of performers. Like Beckett, he imagined every detail of his plays on the stage. Like Beckett, he has to be done well or not at all.

It is almost taken for granted that the words are marvellous – but why should it be? Yeats worked out a kind of verse that can hold its own on stage, a poetry that is clear and robust without losing its mesmeric beauty. That opening of At the Hawk's Well that Beckett parodied is stunning in its sheer evocative power:

I call to the eye of the mind
A well long choked up and dry
And boughs long stripped by the wind,
And I call to the mind's eye
Pallor of an ivory face,
Its lofty dissolute air,
A man climbing up to a place
The salt sea wind has swept bare.

But it is not just about the words. Yeats didn’t need theatre if it was to be a mere poetry recital with costumes. He needed it because it is, literally, where the action is. The idea of action is central to Yeats’s thinking, and what drew him to the stage is what could happen on it.

And what happens in a Yeats play can be startling. Purgatory, for example, verges on the lurid. Its material is the rough red wine of sex and violence: a woman's lust for her groom and their son's murderous determination to extirpate her sin in blood. Yeats's genius is to distill that red wine into a fine but heady spirit, a short, incredibly potent theatrical essence that goes straight to both the head and the guts.

If we strip them of the rhetoric that obscures them Yeats’s plays are serious attempts to address the situation of theatre in a modern world of disembodied imagery. His holy theatre is a response to the spread of “realistic” images through cinema and photography. And it is a response to the emergence of a secular society, trying as it does to make theatres the new churches, places where mysteries are explored through revivified rituals. Those ideas are, if anything, even more urgent in our digital and secular culture.

It seems shameful, therefore, that Yeats the dramatist still gets such a raw deal in his own theatre. There has been no concentrated exploration of his plays on the Abbey stage since James Flannery’s Yeats festivals of the late 1980s and early 1990s. Someone needs to have enough faith in Yeats’s artistry to decide that, in spite of himself, he might have made plays good enough not for artistocrats or pickpockets but for real live audiences.

Fintan O’Toole is Literary Editor