You are offering a solution to something that is not a problem, and you should probably question why you think that / where this ideology is coming from.
You need resources and work to care for your family. The fact that in some cases you are 'paid' (i.e. you have to trade labor) is completely irrelevant. Beaver families are not paid by anyone to care for their home and family.
You could, and can, completely trade out your labor such that you 'care' for your family by being a couple of lawyers completely outsourcing the work of raising your own kids to strangers. At which point I think you've failed as a civilized society. You're only acting as economic agents maximizing profit, and your country is not a country anymore, but an economy. I think America is already at this stage, and that's not a good thing.
Beaver families are not charged rent, money for food, etc.
Just because housework isn't recognized, doesn't mean it doesn't add value to our society. But it's not priced, and it's not taxed.
At any rate - the interesting part is, if we say there's something like five hours of work every day to run a home - how come men seem fine with dropping that in favour of paid work, and women not?
There's a limited few months of giving birth to a child that only women can do, but we see that disproportionately women seem to end up doing much more. Sure, we can simply reduce the amount of unpaid work, by paying people to clean, cook and watch children - but that doesn't answer why not doing so affects women disproportionately from men.
One plausible explanationis sexism; that our society isn't equal.
You need resources and work to care for your family. The fact that in some cases you are 'paid' (i.e. you have to trade labor) is completely irrelevant. Beaver families are not paid by anyone to care for their home and family.
You could, and can, completely trade out your labor such that you 'care' for your family by being a couple of lawyers completely outsourcing the work of raising your own kids to strangers. At which point I think you've failed as a civilized society. You're only acting as economic agents maximizing profit, and your country is not a country anymore, but an economy. I think America is already at this stage, and that's not a good thing.