Bad ideas refuse to die; they just wait patiently for the next manifesto. I thought this line was a bit cynical the first time I heard it from a jaded special adviser. But having lived through several resurrections of the hoary old myth that building new grammar schools would boost social mobility, I’m beginning to see the point.

It was London’s mayor, Boris Johnson, who stirred the pot this week, declaring that scrapping the 11-plus had been a “tragedy” because selective schools were a “great mobiliser and liberator for many people” – which will be music to the ears of those many Tories who grow misty-eyed over 1950s grammars and the wave of working-class talent they supposedly unleashed.

The defence secretary, Michael Fallon, has already backed proposals for a new grammar “satellite” in his Sevenoaks constituency, spun off from an existing selective school. Theresa May has given an interestingly guarded welcome to similar proposals in her Berkshire patch. Why, it’s almost as if there were an election looming, in which the Tories were threatened by some sort of nostalgia-seeped rightwing party keen to bring back grammars; because it sure as hell isn’t justified by the evidence.

Nobody sensible denies there were individual grammar school kids who rose from grinding poverty to greater things. (Nostalgia conveniently obscures the many thousands who didn’t.) But the facts don’t lie. In still selective Kent, poor children do worse and rich ones better at GCSE than in comprehensive counties. David Cameron was right to face down his rightwingers seven years ago and say it was “delusional” to think a Tory government would build new grammars. And as education secretary, Michael Gove may have allowed existing selective schools to expand: but he rightly rejected a previously proposed Kent satellite and argued that, when it comes to social mobility, selection is basically a big fat red herring.

The great gift Britain gave the children of the 50s and 60s wasn’t some exam but an expansion of managerial and professional jobs that created more room at the top for everyone. But now the top is shrinking, everyone’s fighting to hold on to what they have, and schools are becoming their weapon of choice.

The blunt truth is that modern grammars aren’t about shattering class barriers but about reinforcing what Americans call the glass floor, the phenomenon of parents who have clawed their way up fighting to ensure their children don’t fall back down.

I say this having been through a grammar myself, with all that entails; hockey sticks, Latin and years of persecution on the bus for going to that stuck-up cows’ school. We don’t live in a selective county now but if we did, I have a sinking feeling I’d end up sheepishly entering my offspring for the 11-plus like all the other panicking middle-class mothers. Parents see grammars’ dazzling results and oh-so-polite pupils, and principle flies out the window. Politicians know that, and back off. And so the demented arms race in places goes on.

Friends with children in grammar counties report an exodus from state school to prep at seven – the rationale being “pay now, get their secondary education free” – or else years of intensive, expensive tutoring. Parents who can’t afford to compete increasingly don’t see the point in trying, which helps explain why a tiny 2.5% of girls at my Essex alma mater take free school meals (the national figure is 18%).

So I was pleased last year when my old school joined grammars from Birmingham to Buckinghamshire in ditching the 11-plus for the supposedly “tutor-proof” CEM test, designed to distinguish better between raw talent and the expensively coached kind.

If grammars could become genuinely meritocratic, transforming the prospects of bright kids regardless of background, then they’d still stand accused of depriving comprehensives of talent. But at least a grown-up debate might follow on how best to stretch gifted children without disadvantaging others.

So it’s awkward to say the least that next week grammar school heads in Buckinghamshire will be reporting that, in the first year of the test, fewer state-educated applicants passed than in the bad old 11-plus days. Were private schools, facing a threat to their business model if they could no longer boast of getting children through it, just quicker to get the hang of the new exam? Or could it be that, rather like Oxbridge colleges struggling to attract state school applicants, grammars are trying and failing to tackle something that begins way, way downstream from them?

The sociologist Leon Feinstein’s study children’s developmental abilities at 22 months and then tracked their progress to adulthood will by now be wearily familiar to many, but it bears repeating. The surprise was that children from wealthy families who were deemed low ability as toddlers didn’t just catch up: by the age of six or seven they had overtaken even the brightest children from the poorest backgrounds. By 11 it’s asking an awful lot of one exam to unpick the complex mix of parenting, schooling, lobbying for extra resources and attention, and who knows what else, that stops these children falling through the glass floor.

So if social mobility is the problem, grammars aren’t the solution. But arguably neither is scrapping them, since – even if you could somehow get a political mandate to scrap every private and grammar school in Britain tomorrow – parents would always find a way to game the system; we’d still have selection by house price, or by willingness to feign religious conviction, or some other ingenious new wheeze.

That doesn’t mean we should give up trying to level the playing field. But it might mean striving to understand better what it is that some parents – whether affluent ones or the immigrant families increasingly driving the improvement in London schools – actually do that makes their kids get on, and whether it can be replicated. (It’s amazing how often lurking in the background of those self-proclaimed 1960s grammar school success stories is a parent to whom education meant everything, tigerishly determined for their children to do better.)

It means improving the schools that deprived kids are in already, rather than promising new ones and being surprised when sharper-elbowed parents snaffle the places. And it may well mean existing grammars seeking out bright, poor kids more actively and reaching parents early on.

What won’t help is yet another pointlessly self-indulgent argument about the 11-plus exam. Shame that’s the one we are seemingly doomed to keep having.