Imagine a British government deciding to apply all its resources to solving one problem. We’re not talking about some run-of-the mill dilemma here. This would be a proper, A-list, head-scratcher of a conundrum: how to meet the cost of social care in an ageing society; how to provide secure, rewarding work in the era of intelligent robots; inequality; climate change. There are plenty to choose from.

Imagine, too, the government giving itself just two years to find an answer. A special Whitehall department is organised for the purpose. The opposition agrees that the mission is the right one, quibbling only over points of emphasis. The full capacity of the state is bent in service to the mission.

Whatever the issue, whatever the question, one thing is certain. The answer would not begin: “First, leave the EU.” Because that would be the most colossal waste of time, effort and money. Half of the two-year period would be spent just deciding the outline of a future relationship with the EU, and the rest would be spent negotiating a deal to make the country poorer and less influential.

Brexit transition deal breaks seven promises made by ministers, say campaigners - Politics live Read more

There is no substantial problem facing Britain to which leaving the EU offers an effective remedy. Even on its own advertised terms, Brexit is a dud. There will still be immigration across porous borders. There will not be an immediate bonanza of free-trade agreements with other countries, encompassing an area “massively larger than the EU”, as David Davis once forecast. The NHS will not be better off by £350m per week. British courts will still have to take account of judgments made in Luxembourg. The Commonwealth will not be a rival forum for the projection of British influence overseas.

There will not be a great anti-establishment catharsis. A project whose most celebrated cabinet advocate is Boris Johnson, and whose most radical parliamentary exponent is Jacob Rees-Mogg, is no nemesis to privileged elites. (Nor, dear leftist Brexiters, does a policy admired by every fascist in Europe and America contain secret passageways to a progressive utopia.)

Theresa May knows she is in the business of damage limitation. She sounds dogged in her resolve to see the job through, but never enthusiastic about the outcome. She identifies the fight against injustice and the restoration of social mobility as her defining political purposes, but has never explained how Brexit practically advances those causes. She has dismissed the counsels of “no deal” from those who would defiantly flounce from Europe’s table. She sees how they point down a path towards ruin.

The leavers deny the economic price of leaving; remainers want to wish away the political price of remaining

But the other path – incremental separation, close regulatory alignment and strategic intimacy, only with diminished market access, additional friction at the border and a surrender of influence – leads inexorably to the question of why we are bothering to do it at all.

Why, indeed? Pour away all the snake-oil claims of the leavers and only one durable answer is left: because that is what people voted for. It is a better argument than many remainers seem to think. The referendum was, without question, a massive democratic event. There is not much mileage for pro-Europeans in complaining about sneaky methods used to persuade voters, and no merit at all in constitutional pedantry around the designation of the poll as “advisory”.

Leave won and there isn’t consistent or reliable evidence that the result would be different if the country were asked again. Some minds might have been changed by the conspicuous political shambles of the May administration, but the process of being asked for a second opinion could also trigger a collective, bloody-minded doubling down. Some would certainly rally around the proposition: “What part of ‘leave’ didn’t you people understand the first time?”

Even if Brexit could be thwarted at the ballot box before next March – in a plebiscite rematch or a general election where the winning party has unambiguously campaigned on a pro-EU platform – the clock would not be reset to 22 June 2016. Another referendum campaign would not bring a harmonious truce to culture wars stoked by the last one. Some former leave voters might not mourn Brexit’s demise. But plenty would feel betrayed and enraged.

I have yet to hear a compelling remain message for people who had never voted before 2016, but who turned out on that June day because they felt that at long last they could push a button and everything would change. What is the pro-European offer to someone who voted leave precisely so that the kind of people who campaigned for remain would have to listen to them for a change? Try the argument out loud: we’re sorry you were angry that remote Westminster politicians appeared to despise your opinions, now please bear with us while we reverse the totemic decision you felt we couldn’t ignore. It doesn’t sound great.

War shaped my childhood – don’t let Brexit risk our peace | Patrick Stewart Read more

That doesn’t make leaving the EU a good idea. It does mean that the nature of the dilemma facing Britain has changed since the referendum in ways that neither side in the argument likes to admit. The leavers deny the economic price of leaving; remainers want to wish away the political price of remaining. Are those costs equivalent? I doubt that the damage done by Brexit is worth enduring just to avoid the hurt and anger that might be caused by aborting it.

Yet that, when we strip it down to its bare essentials, is the choice that now defines British politics: doing the wrong thing for no good reason because there is not a leader or a party that can make the case for doing something else. Of all the challenges that the country faces, of all the tasks that might have received the same intensity of effort, this is the one we have chosen. And to what end? Only so that when it is done, we can truly say we did it.

• Rafael Behr is a Guardian columnist