There can be few routes to fleeting fame with a stronger chance of success than having a big bunch of kids while claiming some state benefits. The latest household to be splashed all over the tabloids hails from Gloucestershire, and comprises 37-year-old Heather Frost, who has recently survived treatment for cancer, her partner, 11 kids and two grandchildren. The justification for the prurient intrusion of the press appears to be that they have, after waiting many years, finally arranged social accommodation in a single house with six bedrooms that may be appropriate to their needs.

Cases like these form a staple ingredient of cheap newsprint. It would be easy to imagine Britain's housing estates to be swarming with the offspring of the hyperfecund, with their mums bent over the kitchen sink, afraid to fart in case another one pops out unexpectedly.

There are 1.35 million households with children in which at least one adult receives an out of work benefit. Of those, precisely 190 contain 10 or more children. There can be very few who are yet to be honoured with their own double-page tabloid feature or their own TV show.

When that number was revealed through a freedom of information request in late 2011, the Daily Mail pointed out that each of those families could be entitled to at least £61,000 in benefits per year. There's no evidence as to whether those families do collect their full entitlements, but if they did that would total £11m in annual benefits. With a total benefits bill (excluding pensioners) of £100bn per year, that means we could stop all payments to those 190 families, and the country would reduce its bill by less than one hundredth of 1%. However spectacular they may be as news stories, economically and fiscally these families are entirely irrelevant.

Media coverage of such spectacularly large families bolster the belief that people on benefits, and young women in particular, pop out sprogs as a matter of course to boost the size of the weekly benefit cheque or to secure a bigger, better house. In fact, official figures show that those 1.35m benefit-claiming households have 2.55 million kids between them, an average of 1.9 children per household – pretty much identical to the reproduction rate for the population as a whole.

The fabricated scandals of the hyperfecund poor sit alongside the myth of families where no one has worked for three generations or the common misconceptions about the scale of benefit fraud. It is often noted that such stories serve a propaganda function, turning poor against poor and creating a public mood that will not only accept barbaric assaults on social security but actively welcome them. Like most such stories, current coverage of the Frost family and their difficult housing arrangements was not graced with a quote from, say, the Child Poverty Action Group or Shelter, but from representatives of the libertarian fundamentalist group the Taxpayers Alliance, who apparently have nothing better to do than stick their noses into the wombs of the poor.

The Sun dragged in Tory MP Gavin Barwell to explain why this case justified the forthcoming benefits cap, although only a handful of the estimated 67,000 claimants threatened by the cap will have a household even vaguely resembling this one. Just why the member for Croydon Central should have informed insight into a case more than a hundred miles away remains a mystery.

There are legitimate ethical and practical questions as to whether people should have large families while unable to support them with anything more than paltry benefits. Such questions are all but eclipsed by the human costs of cutting the financial support offered to such families. The tabloid press has never shied away from moralistic finger-pointing or the attractions of a garish family freak show, but recent years have seen a trend away from a traditional puritanism towards a new morality that rests entirely upon financial demands on the state. Nowhere in the press coverage does anyone ask whether Frost's children are happy, well cared for and healthy, the only issues are the adults' employment status and the (actually rather modest) cost of the newly built house.

We are now lectured on morality, not by fire and brimstone preachers banging a copy of the bible, but by the slash-and burn evangelists of neoliberal economics banging on a copy of the balance sheet.