I think we need to be careful not to see women's role as being the unpaid carer.
In the early days of women's liberation the idea that women should be part of the work force and equal at home was based on a more hippie / alternative way of live.
But simply everyone would work part time, those adults with child care responsibilities would share equalling in earning money and beinga carer.
However, niavely, despite the presence of socialist who could endlessly speak about the perils of capitalism, women didn't reckon with the oportunity for economic exploitatin this created. ie once it became more common for families to have 2 earing adults, guess what house prices rose, so that unless both adults were working full time you couldn't afford a home.
Rather than homes or the family unit benefiting from the flexibility of 2 adults equally sharing, it became a rat race of less time to be a family just to keep a roof over their heads.
The other early, again niave demand, was for locally based, free 24 hour child care. This was not just to allow the adults better oportunities to work, but to allow local children to grow up together. But as we know this never happened and the childcare needed to allow both parents to be working now costs more than many can earn.
And we are now trapped in this exploitative situation where basics costs are so high most people have to work long anti social hours.
And no I dont think the solution is for older people to be unpaid carers either of children or those who need personal care.