If you want cooking, cleaning, and childcare so badly, why don't you volunteer to do it instead of telling women it's our place. I think I'll take my job over being a man's property.
I help watch my nieces and nephews when needed already anyway, I'm very stubborn about keeping my living space organized and sanitized(in fact i cleaned my grandparent's entire house of mold(they are hoarders too so it involved tons of lifting/reoganizing)), and I've been into fitness/athletics my whole life, which entails learning to cook healthy meals.
If a women were to ask me to come do any of those things for her I would head right over enthusiastically and I don't expect anything in return either as long as she kept me company. This applies regardless of whether I'm romantically interested in her.
People should have the freedom to choose how they live their lives; they should be able to contribute to society in any way they please.
Suggesting that assigning jobs at birth is superior to our current system is rather silly. Yes, we have new problems to solve by ceasing that behavior, but regressing isn't the solution.
I do agree that we don't need two people per household doing bullshit jobs like selling advertising.
But civilization is perfectly capable of decline and disaster even if we were still organized around single income households. So what if out our children have good nutrition, if we are faced with total environmental collapse or nuclear war?
Or you could say that women choose to work for money. The concept of single earner households can indeed work very well, but it has to be a choice of those involved regardless of gender. There are other possible arrangements, too: more communal living, part-time work, inter-generational arrangements, for example. And a true UBI.
That is, at least to me, a very interesting way to describe a patriarchy that was backed only by bible interpretations for centuries.
EDIT: "interesting" should be pronounced with a strong, British accent.
Now we make women work for money, but the total amount paid across all workers is roughly the same. (Wages have been flat for 40 years, mostly because we have twice the "paid" workers—men AND women—but consumption is basically flat.)
It's regressive. Women have ALWAYS "worked" [0], but prior to the financialization of Western culture, that "work" was—as you pointed out—on activities that we can't put a price on, things like:
* building happy homes and families
* proper nutrition, which is extremely time consuming even today
* birthing and raising children (women had universal "time off" to have kids until we put those same women to work making widgets)
* helping out other families in the local community
* building and maintaining community institutions, schools, churches, etc.
* helping others in humane, non-financial ways where there isn't any money to be made
We've given up a lot of these things just to keep wages down for the Capitalists. At least the rising inequality over the last 40 years shows someone benefited. Just not us, or our children, or our communities.
Decline is a choice.
[0] I hate that our culture only values things that can be expressed in terms of money. Calling what women do "work" (or as the OP calls it, uncompensated "labor") is demeaning to women. What women do day-to-day is vastly more important than whatever bullshit men have to (gladly) do to build and maintain civilization for their families.