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Musing on what WERE the 'jobs no {American} wants to do,' it seemed that they are the sex-role defined jobs from previous decades. House-cleaning, child-care, laundry... these were done by women; lawn-mowing, car washing, seasonal preparations (tree trimming, lights, eaves cleaning)... these were done by men.
Women with full time jobs had less time / energy / interest in home chores; men saw that women were getting help, so they sought the same and many family chores became the 'jobs no {American} wants to do.'
People who do household chores are re-enforcing the shared relationship of the family {however that is defined) and maybe that is what contributes to more sexual sharing.