Its not necessarily that people don't want to but that society is set up in a different way now days.
My mum grew up with her mum doing all the caring and grandmother next door. When my own grandmother became unwell she moved in with us, my mum did the care. It was unthinkable that anything else would happen.
However with my grandmother it was a whole different scenario. She had dementia and by that point my mum needed to work. So a really difficult decision was made about care.
When it comes to my own parents and inlaws my capacity to care for them is much lower. Firstly there are smaller sibling groups and much less local. We are the closest to my inlaws and are 1.5 hrs away. I cant move to inlaws area and they cant move to ours. I simply dont have the ability not to work to complete care.
Combined with people living longer (my dgran is still about at 100, being cared for by her 80 year old child), especially living longer with more and more complex health. People are having children later so im now in the position of caring for an 80 year old whilst still having a toddler.
Its the same reason people are using things like nursery's when they used to stay home, or rely on family support.
In a not too distant future caring responsibilities were held by the women who tended to be working a lot less
For us even things like food shops are hard, I can order an online shop but its hard to have someone present for a whole delivery slot to put it away. Care services arent really set up like that
Basically Care services arent set up for what the modern world has become