I suspect PNAS would not be interested, but you could run it by @jaricheson, who accepted the Mutz paper. I do not read PNAS religiously, but the only failed replic I ever saw there was Wms&Ceci's no sexism studies. This compares it to the prior Moss-Racusin paper. pic.twitter.com/avvH4O8vjd
A major factor driving the gendered division of labour and household effort is technology. Tiny differences in comparative advantage such as in child rearing immediately after birth can lead to large differences in specialisation in the market work and in market-related human capital and home production related work and household human capital (Becker 1985, 1993).
These specialisations are reinforced by learning by doing where large differences in market and household human capital emerge despite tiny differences at the outset (Becker 1985, 1993). This gendered division of labour and household effort is hard to change because large payments must be made to influence choices about care giving by highly specialised people with large but different accumulations of market and household human capital.
From a luck egalitarian perspective, many of the differences in earnings and occupations flow accidents of birth in deciding gender and who parents might be. Social inequalities that flow from brute bad luck call for interventions to put them right, if they work.
Many laws already make up for brute bad luck such as job protections while on maternity leave, and government funded parental leave pay and child care subsidies. Employers can do little to redress these accidents of birth nor do they have sufficient resources to put them right. For this reason, for example, parental leave pay is usually taxpayer funded rather than employer funded.