You can take a prime minister from the Home Office, but you just can’t get the Home Office out of the prime minister. Under pressure to sing a song of unalloyed Brexitism, Theresa May goes for the tune she knows best, the one on which her career was founded, the one about getting tough on immigration.

But these aren’t the good old Home Office days, belting out “Go home” from a van. May is in a much more complicated job now. She is limited to rejecting the part of the EU’s proposed framework for Brexit transition that would allow continental citizens to start acquiring residency rights even if they move to the UK after 29 March 2019 – the formal departure day.

The European commission’s view is that transition extends to nearly every aspect of EU law and practice, including free movement of labour. So the point at which residency entitlement expires shifts forward too. May is happy to smudge the line between in and out in order to achieve a “smooth and orderly” departure in every respect except migration. She sees that slippage, when it comes to limiting foreigner headcount, is too toxic. It would substantiate the claim that transition is “Brexit in name only”. For May, a deal that doesn’t deliver quick border control is a betrayal of the referendum result.

There are many strange and wrong things about this judgment. First, in the case of Conservative party management, it is hardly an issue. I have spoken to many Tory MPs this week, all of whom are deeply dismayed by their leader’s handling of Brexit. None of them mentioned immigration. When you dig below the crust of general discontent, the fault line is between those who want some kind of customs union to avoid a crunching disruption of trade flows with the EU (the Treasury view), and those who cannot stomach a customs union because it limits Britain’s capacity to strike trade deals with non-Europeans (the anti-Treasury view). In that debate, neither side is bothered if EU citizens get a few months’ extra leeway to get settled in Britain, if that is what they really want.

Then there’s a second problem: May is defending a line that her own government has already surrendered. Only last week, Philip Hammond, the chancellor, David Davis, the Brexit secretary, and Greg Clark, the business secretary, signed a joint letter to business leaders promising maximum continuity of existing arrangements in transition. It has explicit reassurance on the movement of labour. They wrote: “Citizens will continue to be able to come and live and work in the UK, with no new barriers to taking up employment.”

If May wants to restart an argument that her cabinet and all 27 leaders of the rest of the EU thought had finished in December, she will almost certainly lose, and waste a lot of time and goodwill in the process. It is worth noting also that May has nothing to say about how limiting the entitlements of EU citizens in transition affects Britons wanting to live and work abroad after March 2019. She cannot conceive of free movement as a reciprocal benefit, only as a cost inflicted by “them” on “us”. It would not occur to her that pinching stingily at the rights of foreigners diminishes UK citizenship too.

There are, of course, many voters who care much more about immigration than trade. Perhaps the prime minister thinks she can reassure them directly, speaking over the heads of her fissiparous party. But this move reeks of panic and exhaustion. It is a tired ditty scraped out with anxiety-gnawed nails on the bottom of the ideas barrel. It is the muscle memory of a broken leader staggering forwards on autopilot, with no capacity left for imagination or original action. It is a zombie announcement, disinterred from the past. It is the pitiful ghost of a happier, stronger, more stable Theresa May at the Home Office, when she had plans and felt she was in control.

• Rafael Behr is a Guardian columnist