I don't think it's universally true that old people generally dropped dead without needing care above and beyond the care you'd extend to a healthy relative you loved, or that they weren't cared for by their families well into advanced old age. It certainly doesn't ring true for my (Irish) family.
One grandfather died in his 70s of cancer, well before I was born. The rest lived to 85, 89, and 93. All those long-lived grandparents lived at home and were cared for by their children / family in their old age. Two were pretty infirm when they died. One took to bed for the last two weeks of life.
The burden - yes, that is very much there for many nowadays, and it is an enormous problem. But let's not pretend it wasn't a problem before now.
In my dad's family there was always a designated 'minder' daughter, for generations, whose life purpose was to mind mamma, and in my mum's family, the older generations lived on the farm and were taken care of by the wife who married in.
We have moved on from women confined to the domestic sphere and denied choices, to women allowed to and encouraged to - and in many cases forced to - be wage earners, but the expectation that women will also shoulder all the family burdens remains, and not just relating to care of elderly relatives - women come home and do the second and even the third shift when they close that front door behind them, kick off their shoes, and whip off their bras. Cooking, cleaning, attending to school stuff, laundry, emotional support, getting up in the night when toddlers cry or kids are sick...
The rest of society really hasn't caught up with the reality of women's lives. I'm glad the issue is being discussed. I think it needs to be seen in its wider context.