Interesting discussion. The state has only offered help for the care of the elderly very recently in historical terms, less than the last 100 years of human history - a bit like most of the other state assistance we have today.
Two significant things come into play for me when thinking about this issue in broad terms. First, is that societies should be responsible for those who cannot be responsible for themselves, secondly, being personally responsible. Most of us know that we will be born, live our 80 odd years and die. There is a fairly well established trajectory there and a reasonable understanding of what those years will most likely look like. We need to ensure children are educated in such a way that they can be responsible for their own lives, wherever possible. There is a discussion to be had about how well that is done these days.
Clearly, shit happens and there is a case to be made then about the society we live in supporting us. Some people will never be able to help themselves and they need the most help and from my own perspective the state has a role there.
However, if we want cradle to grave care that is free at the point of delivery, then we all need to commit to that as a country and pay the tax that is necessary to fund that kind of care. There are countries, such as Denmark, with remarkable social care systems but their population pay huge amounts of tax for that.
Here in the UK we sit, like a lot of countries, with a neither one thing nor the other kind of system. I wonder how long that will be sustainable. Our adversarial political system, mean that the Tories edge us towards a more capitalist, free market approach and Labour edge us towards a more social welfare, interventionist approach. We wander endlessly along the middle ground. Maybe that is a good thing or maybe it means we get the worst of both worlds.