I can see why those families that have the luxury of a stay at home parent may have a benefit, but I think it’s unhelpful (for both men and women) to enforce the gender stereotype that women have to be the ones to stay at home and the men have to work.
I know several families where the mother has more skills/more valuable work and works full time to support the family, while dad stays at home. All family parties are happier and better off with this arrangement but “old fashioned sexist” values say they should not.
In fact, in the sutta you quote it says nothing about who should stay at home and who should work, and I think reinforcing sterotypes about this can actually do harm to both sexes.
Perhaps if women can stop being trapped/coerced into their traditional gender roles, they can study, become scientists and contribute to innovations that reduce the environmental burden of climate change. If you really want to get environmental, educate girls so they don’t become mothers (too many too early) and contribute to our existing burden of overpopulation. Even better give them the equal support to become nuns and be free of samsara forever. Any ‘solution’ to make lay life in samsara better is a delusion.