Eyre did exactly that, helped by a 13-strong working group, more than 200 expert witnesses and 1,200 members of the public who wrote in with their views. The outcome, a 150-page report, has sat on Chris Smith's desk since June, and we have little indication that much of it has yet sunk in.
Calm, lucid and balanced, the report offers the most comprehensive set of proposals ever for the capital's three main lyric theatres (Coliseum, Covent Garden and Sadler's Wells) and the companies that play in them. But from most of the media comment and the actions of ministers, you might imagine that nothing mattered except the Royal Opera company and the Royal Opera House. No wonder Eyre says that he wishes people would read the report in its entirety: "The arguments I make - in particular, for funding - cannot be taken out of the context of the entire argument."
So what happens? Before giving his own response to Eyre's ideas, Chris Smith seeks the comments of the most affected companies. Fair enough, but then ignoring all other aspects, he gives his blessing to the plan to close down the Royal Opera, and maybe the Royal Ballet too, for a year. Nor does anyone seem to have taken account of Eyre's strong recommendation that Covent Garden must stop its arrogant habit of going direct to government, which he condemns as demoralising to other arts organisations.
More arrogance: nobody from Covent Garden (nor the Arts Council or the Department of Culture) thought to give any warning to Sadler's Wells about cancelling most, or all of the six-month season booked there for the Royal Opera and Royal Ballet next summer. The first that Sadler's Wells' chief executive, Ian Albery, heard about the decision was from a journalist.
The Wells, rebuilt primarily as a dance theatre, had agreed only reluctantly, under Arts Council pressure, to allocate many months to the Royal Opera. It will be "in your best interests", they were told - which is manifestly now not the case. What adds injury to insult is that by dropping out, Covent Garden left an enormous hole not only in Sadler's Wells finances (which will be filled, we are told, although with no details of where it will come from, or when), but also in the otherwise exciting programmes for the theatre's reopening year. Some of this will be made good, thanks to Sadler's Wells' high standing in the world of dance and the ingenuity of its programming director, Nigel Hinds. But understandably, they feel sabotaged.
Even without this problem, the redeveloped Sadler's Wells would have been in a tricky position. Its only public subsidy is pounds 220,000 a year from the London Arts Board. As Eyre says, without substantial additional funding, the Wells will have to pass on its costs to incoming companies and make itself too expensive for many of them. For instance, it already seems that next year's British tour by the Mark Morris dance company may have to omit the Wells.
Similarly, the Coliseum, another excellent theatre for dance, with a larger seating capacity, is willing and able to accept more visiting companies. But its costs have been notoriously high, and Eyre's recommendations about sorting this out have got nowhere so far.
And by promising extra money to Covent Garden - even while they do not perform! - Smith and the Arts Council have less room for manoeuvre, so the enhanced dance seasons envisaged in these other London theatres are in danger.
Luckily, many of the other points which Eyre raises involve little or no cost. In some cases, he indicates potential savings: on management salaries at Covent Garden, for instance, which he found way out of line with comparable companies; on unnecessary use of expensive consultants and advisory boards; and on lavish productions where his own theatrical experience indicates the possibility of achieving results with more imagination and less cash.
He sees an overwhelmingly strong case for setting up a co-ordinating group of the three big lyric theatres to look at issues such as repertoire, labour relations, working practices, and advises that co-operation should be a condition of receiving subsidy. As for present Arts Council policies which restrict touring within specific regions and hamper London seasons by regional companies, he calls them "a bureaucratic and damaging nonsense".
But perhaps the gravest problem left unsolved is the future of the Royal Ballet. It is understandable that dancers rebelling against the Royal Opera House board's decision to suspend activities next year want to break away as a separate entity. The Royal Charter actually makes provision for this in such circumstances. But where would the capital come from? Even more crucial is the question whether the present directorate of Anthony Dowell and Anthony Russell-Roberts, who have presided over a period of decline, have the imagination or the strength of purpose to succeed alone.
As Eyre mildly remarks, "the Royal Ballet's repertoire now is not as rich as it should be". He suggests a need to develop a clear artistic vision and to draw on its own rich heritage, which has been seriously neglected. At the same time, he points out: "More significant new work is essential if the company is to maintain its leading presence in the international field and to continue to contribute to the advancement of the art form."
Turning policy around is not going to be easy, whether the company breaks away or stays at Covent Garden. And if it does stay, the one issue on which Eyre seriously goes astray is in believing that parity of status between ballet and opera there, which was a condition of the National Lottery grant, can be achieved by an administrative set-up that puts the Royal Ballet's artistic director and music director under the supervision of their opposite numbers at the Royal Opera.
So thank heaven for the one good, positive deed among many recent disasters - namely the ROH board's decision to appoint Michael Kaiser as its new executive director. His recent (and very hands-on) achievements with American Ballet Theatre can give real hope for improvement towards a better balance here.
One major point from Chris Smith's own pre-Eyre proposals seems to have been forgotten; that is, renaming the Royal Opera House. Too many people appear to think it is the Royal Opera's House, which helps to account for the way ballet has been neglected by most commentators and even by the theatre's own management. To call it officially just Covent Garden Theatre, as Smith suggested last November - or even, if sponsors must have a grander title, Theatre Royal Covent Garden - would focus the change of attitude that is essential if the rebuilt house is ready to deliver what it has promised. Go for it, Mr Smith, please.