>It doesn't account for differences in industry, job title, experience, etc. It's super broad.
It also doesn't account for full time covering a wide number of hours worked. Full time can be 37 hours a week or 45 hours a week, can comparing them as both just being 'full time' misses quite a lot.
>This is in large part because care for family members(children and elderly parents usually) is more often foisted upon women in our society than on men.
How it is more often foisted upon women? The social pressure on men to take deadly jobs and to work longer hours is equal to the social pressure on women to choose careers where they can take time off and be with their kids. If anything, I rather be with my kid than stuck an extra 20 hours in the office... one of these pressures is for something most people find more desirable than the other.
>We need to de-stigmatize flexible schedules.
So are we aiming for more men to take flexible schedules or for pay to not suffer when someone takes flexible schedules? Because if you want the former, it is more about the pressure to earn than the stigma on flexible work schedules. And if it is the latter, how is this fair to the people who don't get the flexible work schedules? I think the deeper problem is why are women forced in the child care role and men into the bread winning roles and how to fix that (which you do mention).