Uh, dude, you can shop, cook, and clean even if your breasts don't produce milk and stinky diapers give you the sad.
Sweden does it right. There give so much paid maternity/paternity leave that I won't even tell you how much because you'll start crying hysterically. The "catch" is that they mandate that it is split between the two parents. Not a 50/50 split, but one parent can't take all of it. The point is that in practice the Dad takes some paternity leave all by himself and therefore is nudged into getting some experience being the primary caregiver for a bit.