I would prefer that families provide these services (and, therefore, the state focus on the formation of strong families).
So, under your plan, I should dread getting old.
I have no children. I have never wanted them, and it is a relief that I shouldn't have any (medical wise). Besides, it'd be risky at my age anyway. I have a spouse, but otherwise have no family on this side of the Atlantic. My father died, my mother is getting older, and my siblings both have families that include children. I'm supposed to burden my family with my care? I'm not sure immigration would let them come over here and if I go there, I have no health coverage. Sure, my spouse would take care of me. But at what cost? Quit his job and actually make less money, right when medical expenses go up? What if he's already died or disabled? Well... I'm screwed.
I'll add this: I did a lot of care for my ex. It was mental illness, but still. And I felt freaking trapped, and it took longer to leave. My grandmother married a man who had a stroke a year later. He became abusive, but she was scared to leave due to getting in trouble for abandonment (this was in the late 90's). She was stuck for a while. Your plan does nothing to help the folks that are in bad situations. Sure, you might want strong families, but the reality is that not every family is going to be that way.
The market is too brutal for most of this work and the state, in addition to general incompetence, lacks the moral authority to do so, especially when hard decisions must be made (e.g. when homelessness is driven by mental illness.)
Sorry you live in such a country, and glad I no longer do. The country I live in tries to do these things for folks, provides healthcare and elder care. It isn't perfect or anything, but they are doing more than the states did and they are trying to improve things slowly. The state doesn't have to be like that, and you can change it. Vote for different people. And if they don't do the stuff, vote them out of office.