It's not a superficial metric when it's so pervasive over time and amongst a variety of cultures. If you had a sample of 100 couples, maybe, but when it's millions of couples, I don't think so. And it's not just housework, it's also childcare, and eldercare. It's the kinds of things that are now classified as "emotional labor" such as making sure there are teacher gifts at the end of the year and buying cards for relatives birthdays. These are all really, really well documented.

And if "breadwinning" women are mostly just women who want to have the final say in the family, they why are they overwhelmingly doing the vast majority of the housework, with this increasing, the more they outearn their partners?

“Drawing on a sample of 23,088 mothers living with children under the age of 13, they found that married and cohabitating mothers racked up approximately 3 hours of housework per day, compared to 2.5 and 2 hours respectively undertaken by divorced and never-married mothers.

Married women also get the least sleep and the fewest hours of leisure-time. Interestingly women who live with a male partner but haven’t married him have more leisure time — an extra 35 minutes per day — compared with married women.

This suggests that it’s not just having a man around that’s the problem. Rather, the issue seems to lie with the expectations that come with being his “wife”.”

The Sydney Morning Herald

Plus, men and women have the same understanding of what is clean and what is messy. It's just that women are judged and penalized more if they don't keep a space (even a shared space) to a certain standard.