But now, following the announcement of his appointment as artistic director of the Almeida Theatre in succession to Michael Attenborough, with effect from August this year, we must ask: will he ever want to? He's still only 40 years old, so there's still time. But the Almeida seems a perfect place for him.
Why? In a much smaller organisation he is paradoxically left far more room for manouevre and indeed empire-building. As he's shown with his work at Headlong (the touring company he's run for eight years), he can still make a big impression within the major theatres, as he's done at the National with Mike Bartlett's Earthquakes in London and Lucy Prebble's The Effect.
And ENRON was a superbly engineered collaboration with both the Chichester Festival Theatre and the Royal Court. No other director has proved so adept at pitching tents in various camps while maintaining a singular vision and purpose. You can easily see the Almeida becoming a creative crucible for whatever is really happening next in our theatre, no doubt starting with Goold's own production of the musical American Psycho there in December.
There's another important factor. The Almeida is the most magical small theatre. Its brick walls and peculiar intimacy - with epic potential - has no equal in London. Only Peter Brook's Bouffes du Nord in Paris comes close, and Goold, like so many of our leading directors, is an ardent disciple of the great, wise, and always approachable, guru.
He demonstrated his enthusiastic response to the Alemida's features in his stunning production of The Last Days of Judas Iscariot in 2008. This is a theatre where you can go big while staying small, paint a universe while attending to detail. Let's face it, there are huge technical problems in producing work in both of the National's bigger houses, and the shortcomings of the new Royal Shakespeare Theatre are already apparent in the desperation, for instance, in the design for the new Winter's Tale.
Even Adrian Noble's vigorous new production of The Captain of Kopenick in the NT's Olivier is bedevilled by uneven sound balance between microphoned and "live" voices and music; it's just awful, actually, and something critics never get round to discussing. And the RST in Stratford is, quite obviously, a nightmare for the basic business of blocking.
In a theatre like the Almeida, you can just get going without worrying about these practical details. Everything an actor says or does can be easily seen and heard. And the multiple possibilities of design and presentation flow from the building's human-scale rigidity as much as its character.
The last year or so have been a bit rocky for Goold, even though Headlong has continued to flourish and The Effect has been a terrific hit. Tied up in an American movie, True Story, which seems to be shrouded in secrecy, he pulled out of his own pet RSC project last year, the Troilus and Cressida jointly produced with the Wooster Group in New York. And then he withdrew from his ENO commitment this spring to direct Alban Berg's Wozzeck.
This was not good news, not least because both projects were, on paper at least, ideally suited to his talents for setting himself a problem, or a mountain to climb, and then solving it, or simply running up the north face.
But redemption is now at hand. Tribute is owed to Attenbourgh, too; he has run the Almeida so well for the past ten years, maintained its reputation and now frankly clears the decks for something completely different but innately appropriate to the Almeida's traditions.
These have covered the experimental, internationalist flavour of Pierre Audi's founding regime, followed by the glorious decade of Ian McDiarmid and Jonathan Kent, and Attenborough's own record of mixing vital, quirky, often underrated new plays, with a diet of adventurous, if not always showily brilliant, revivals and classics.
Above all, Attenborough has always been a great theatre manager, wherever he's worked. In a real sense, he's facilitated the arrival of Goold, who could now embark on a decade of unrivalled innovation and excitement. Let's hope so, anyway!
And what about the RSC and the National? Ideally, they should be run by much younger people, but the size of the job has become so great that there has to be an element of safe, middle-aged hands about any appointment. Gregory Doran will almost certainly stay in situ for ten years.
But who will succeed Hytner at the NT? I wouldn't bet against a Stephen Daldry come-back, but the clear favourite remains Dominic Cooke. Whoever it is, he or she (or they?) will probably end up envying the comparative freedom and flexibility Rupert Goold will be enjoying down Upper Street at the Almeida.