Earlier this month, the New York Times ran a news story that didn't contain much news. Britain's National Theatre, Pat Healy wrote, has succeeded in business without really trying. Well, not trying to appeal to the marketplace, that is. Through a strategy of artistic boldness backed by populist shrewdness, the piece argued, the National, under Nicholas Hytner, had found an unlikely cash cow in War Horse (to mix farmyard metaphors), which was still running in the West End and banking $1m a week in its Broadway incarnation. How, Healy breathlessly asked, did Nick do it?

The question I wish he had asked is slightly different: "How could it happen in America?" Hytner's winning game plan is old news: funding his organisation with a mix of government money and corporate cash (the Travelex tickets); trusting audiences to navigate seasons that mix classics, new dramas and more experimental fare; and actively engaging the wider culture and media – even if that means stirring up a critics-are-dead-white-males fracas. We New Yorkers who go on pilgrimages to the National – who salivate over a season that includes new McPherson, revived Wesker and Beale and Jennings sharing the stage – have known for years that Hytner is a remarkable artistic director.

But to answer the unasked question: could we have someone like Hytner in New York, or Chicago – or anywhere, really? No; and if not yet, then possibly never. Our best artistic directors are probably fine managers and dependable fundraisers – but can any of them hold a candle to the current boss of the National? Or other British artistic directors such as Dominic Cooke of the Royal Court or Michael Grandage, who's just stepped down from the Donmar ? Despite the enormous potential of the American theatre – we have (some) federal funding, wealthy donors and corporations and plenty of talented writers, actors and directors – the fiscal and artistic resources never seem to constellate around one person or company with sufficient intensity to create real momentum.

Money plays its part. The National's annual income is £70m, which includes an Arts Council subsidy of £19.6m, equivalent to 28%. Of course that subsidy will decrease over the next two years, down to £17.4m in 2012–13, at which point it will be less than a quarter of the National's projected total income. And despite the cuts, the National's budget dwarfs that of New York's largest nonprofit producer, the Roundabout Theatre Company, which runs on approximately £33m per year. Although the Roundabout programmes five stages – three of them on Broadway – it produces a third of the shows the National does.

But the biggest gulf between the two companies is in artistic quality; I seriously doubt that the very well-compensated Roundabout head Todd Haimes would want me to do a quality comparison between his 2010-11 season and the six worst shows the National presented last year. So cash matters. But so do personality, imagination and taste, and this, I fear, is where our big nonprofits come up short. Yes, Lincoln Center Theater, under the direction of André Bishop, and the Public Theater, under Oskar Eustis, offer solid work every season. But how many of their world premieres have international reach? Why aren't they commissioning world-class plays that the National or the Royal Court might want to import, as we have done with War Horse? Where is the play about the BP Gulf oil spill? Where is the play from inside the Tea Party? Where is the bold revival of Strange Interlude? Where is a sprawling historical comedy about utopian communities in America? John Guare's A Free Man of Color – a dazzling piece set in 19th-century New Orleans, produced last year at LCT – is the exception that proves the rule.

When we bemoan the lack of bold leaders at our theatres, we hold up Joseph Papp (1921–1991) as the Platonic ideal of the feisty, innovative tastemaker. Papp certainly made his mark, founding the Public Theater and offering free Shakespeare in Central Park each summer. But even he had his detractors. In a 1974 essay for the American Scholar, critic Stanley Kauffmann traced Papp's remarkable ascent with a mixture of wonder and disappointment, concluding that Papp's chutzpah had little substance to it. "If we disregard the big commercial managements as irrelevant to our discussion," Kauffmann wrote, "then Papp is the only person who has made a considerable mark in the theater – in any American or European theater that I have seen or read about – without extraordinary talent, without exemplary taste, without an esthetic imperative, without intellectual distinction." I don't know if anyone has attempted a similar critique of Hytner's reign. But on this side of the Atlantic, even our idols are tarnished.