Sex is the very least of our concerns, the last thing that has to be crossed off the to-do list. Or so I have heard from harassed women in the school playground. Yet sex is the very meaning of life, the cement that glues together every relationship, half our culture also tells us, while the remainder portrays women as a series of orifices to be penetrated.

Perhaps sex is all and none of these things. When people write to experts asking for help, their problems inevitably boil down to: “I want more or less sex, or of a different kind, or with a different person from the one I am currently having sex with.”

This is why the idea of women going on sex strike as a form of resistance is a no-go, although the latest person to suggest one, the actor Alyssa Milano, is right to be appalled by Georgia’s “heartbeat law”, which means a woman could be imprisoned for having an abortion after six weeks of pregnancy. We all get where Milano is coming from – or not coming from – for sex is attention-grabbing.

Inevitably, much whataboutery has followed this oldest of ideas: what about lesbians, sex workers, trans people or women who actually want sex?

What does the withholding of sex do? I always think of Mrs Merton on the three words every man wants to hear: “If you must.” If withholding is a political action, then the go-slow of many long-term relationships – the pressing of the shared snooze button – is, er, radical.

What I really like about this is the strike bit, not the sex bit. If we women want to assert our right to bodily autonomy and our economic worth, let’s stop. Just stop. Do not pick up the kids from school. Do not put the washing on. Do not smile at that man because he is making you nervous. Do not buy the birthday presents. Stop caring, in other words.

For this is the huge inequality globally: women’s unpaid work, which is mostly caring for others. We used to call this the domestic-labour debate, and some on the left vaguely recognised it; but the left, just like every other part of life, runs on the unpaid work of women. Work that is seen as voluntary.

Now this debate has resurfaced as an economic consideration. At Davos, that meeting at a ski resort where rich people pretend to care, Oxfam this year put out a report on the unpaid work done by women around the world. It is worth $10tn (£7.7tn) a year, apparently – which seems like a lot of money, but I can’t work it out, as I have a dishwasher to unload, a sick relative to visit, a child to look after.

What would it be like to stop working for free? Most of us would find it hard even to separate our domestic lives from what we feel is just being a decent person. This is how we collaborate in our own oppression. Right now, a wave of young women are flogging housework as a source of self-esteem. Sure, ladies: it is right up there with breast-implant gift vouchers.

The double shift of paid and unpaid work is the bit that women lie about in public – and to themselves. Please don’t bother telling me that men do more. I live in north London in a sea of beards and buggies and fathers buying kale snacks. I still don’t have the time to applaud men for looking after their own children.

In Iceland, on 24 October 1975, women did go a strike for a day. Fish factories were closed. Fathers brought their children into work. Sausages sold out, as that is what men fed their kids. A law was passed ensuring equal pay. This day, which is still celebrated, became known as “the long Friday”.

This idea seems almost like science-fiction now – even the basic notion that women would show such solidarity. Still, we are now in a moment where the rights of women are being rolled back in the US, Poland, Spain and elsewhere. So, it is not sex that needs to be withdrawn; it is unpaid labour. It would bring the world to a standstill. Women of the world, unite. We would not lose our chains; we would simply make them visible. We could be heroes, just for one day.