Are you still waiting for Chilcot? I don’t mean in the literal sense, obviously. Six years on, waiting for John Chilcot and his distinguished panel to say something – anything, really – about the war in Iraq has become a constant of Westminster life. Two elections have come and gone; one by one, key players are retiring from political and army life, and still nothing. The boiling frustration of grieving military families, who yesterday threatened to sue if he doesn’t deliver soon, is entirely understandable.

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But almost nobody is waiting for Chilcot now to make up their mind. Twelve years after the invasion, whichever camp you’ve chosen – Blair the bloodsoaked war criminal, Blair the tame poodle, Blair the honourably mistaken but hopelessly overconfident, or even (niche, but it happens) Blair the saviour of the Iraqi people – your views are doubtless pretty settled. Public opinion calcifies; it’s hard to keep an open mind forever.

Even if Chilcot has, against absolutely all expectations at Westminster, found the smoking gun that eluded everyone else, then millions now wouldn’t even believe in it. Whomever it exonerated or damned, the internet would merely heave with conspiracy theories about why it surfaced now. There’s a grim irony to the fact that those accusing Blair of choosing facts to fit his conclusion are often guilty of the same.

But the Chilcot non-report still has something to teach us – possibly more, indeed, than the appearance of the damn thing ever will. And as an almost impossibly wide-ranging public inquiry into historic child sex abuse, which could easily drag on six years or longer, gets under way it’s timely to consider those lessons.

Nobody hearing yesterday’s Radio 4 interview with Reg Keys, whose son Tom was killed in action in 2003, could doubt that the inquiry has failed to give grieving relatives what they want. Many families understandably want to know whether their children died in a just war or in an illegal one – and if the latter, to see someone punished; but there is no guarantee that Chilcot will definitively answer that question, let alone grant Keys’ wish to see Blair dragged before a court.

The striking thing, however, is that Keys seemed almost wearily resigned to that. Asked what would bring him closure and help him begin to move on, his answer was for the wounds of grief not to be constantly reopened by public debate; he just wanted to be able to “consign Iraq to history”. And suddenly, you were reminded of the way forensic teams painstakingly comb the rubble of bombsites for any scrap of human remains, in recognition of the powerful human need for something to bury.

The soldiers’ families have held funerals, but what Keys seemed to be expressing was a desire to put Iraq in the ground, too; to contain it, if not to forget. While some of the delay has been beyond Chilcot’s control – the death of a panel member, the tortuous negotiations over publishing notes of some Blair-Bush meetings – the prolonging of the agony for the families feels horribly cruel nonetheless.

But if what we have come to expect of Chilcot is essentially some kind of truth and reconciliation process – to help the bereaved come to terms with loss, and the rest of us understand exactly what was done in our name and why – that was not the job he was actually given. The Chilcot inquiry has arguably failed its remit, but its remit was probably not the one you think.

Its official purpose as set out by Gordon Brown to parliament was to establish lessons learned in Iraq to “strengthen the health of our democracy, our diplomacy and our military”; in other words, to avoid repeating mistakes in future conflicts. It was supposed to take only a year, at least partly because such lessons must be reasonably contemporary to be useful.

Since we’ve intervened in Libya and are on the brink of doing so in Syria with the benefit of precisely zero insights from Chilcot, even on these limited grounds it has hardly been a success.

But there was an unofficial purpose to it too, which was more nakedly political. The inquiry was always seen as a way of Brown differentiating himself from Blair, showing willingness to clean out the stables where Iraq remained an issue; but it was at least partly also responding to the very public distress of those who had lost loved ones in action.One wonders how much of that nuance got across in the ten minutes Sir John said he was given to decide whether to take the job.

Now what we’re left with is an inquiry falling unhappily between two stools; reporting neither early enough to be useful (unlike, say, the Mid Staffordshire hospital scandal inquiry) nor late enough to take the long view of history, as the equally interminable Bloody Sunday report did.

What we have come to expect of Chilcot is essentially some kind of truth and reconciliation process

The risk, meanwhile, is that the system can only grow more unwieldy. An explosion in trackable data – emails, texts, communications that would once have been verbal and perishable but now must all be traced – suggests future inquiries will be if anything more time-consuming.

Public faith in “the establishment” uncovering the truth meanwhile is fading, while the never-ending nature of these sagas means good potential chairs shy away. The longer Chilcot drags on, the more reluctant governments become to establish future inquiries.

So why not establish a fiercely independent standing office of investigators whose sole job is to analyse and learn from the state’s mistakes? A squad to be assigned whenever something big goes wrong, roping in specific expertise as required, bringing everything learned in the last inquiry to bear on the next. (After all, the same themes – poor communication, poor management – pepper every report.)

It could include not just elderly judges but behavioural scientists too, capable of understanding why humans make mistakes and what drives bad judgments, alongside data scientists good at sifting vast quantities of information.

And where what’s really needed is to reconcile victims to traumatic events, or apportion blame, then we should have the courage to separate that clearly from the time-limited learning process – instead of heaping everything into one vehicle that inevitably then grinds to a halt. The old joke that we now need an inquiry into the Chilcot inquiry is not, as it turns out, that funny at all.