I think there's a bit of a subconscious feeling that social care is not really as essential as medical, and should all be provided by the person or by family. Buying it in at all is seen as a kind of going private, so a luxury, not a need.
Also it's perhaps seen as worth giving people medical care because some of the people who get that might recover and be valuable, but social care has no such obvious reward for society.
Within that assumption about family is another, of course, that there's an army of middle-aged people, mainly women, out there, who should somehow be the ones dealing with all of this.
Well, dealing with it until they get too tired and old, at which point their reward will be for society to hope they die quickly without being too expensive, just when they'll probably really feel like they've earned a rest and deserve a bit of being looked after.
There are other ways we could recoup money from older people on the basis that otherwise all they'll do is selfishly pass it down to their children. We could start charging for GP appointments after a certain age, so they all get totted up and when the person dies a sum for that is taken out of their estate. We could increase council tax for them on the same basis, and get the money later.
If the important thing as some people see it is to make sure that all of us pay for as much as possible of what we use after a certain age, while we have any funds remaining, because otherwise we might leave money to adult children, then we might as well do that.
Or we could say that leaving money to children is as OK if you need social care as if you need medical care, and that pooling costs would be better.
It would mean sucking up the fact that a minority of rich old people who need a lot of care will then get to leave more money to their children than they would have done with the current system.
It's only the same amount they'd be leaving if all they'd needed was expensive medical care and not social care, though. It might feel less unpalatable if we remember that other rich old people, ones lucky enough not to need a lot of care, will then be paying more than they did before, and leaving less money to their children.