The authors of Spousenomics say that couples are happiest if they divide chores by comparative advantage - that is, if you do what you are somewhat better at. There does have to be some rough balance of the total labor that each does for the family, too.
I am confident that if couples followed this rule, the division of household labor would skew toward a traditional gender division of tasks. Any given couple might divide tasks up in any way at all, and some couples would be very untraditional, indeed.
Nonetheless, the traditional division of labor got to be traditional for a reason. It reflects the skew in the population as a whole of the comparative advantage of the sexes. So be it.