As I read that, I agree with you... Until I realize you meant that to be provided for by others via taxes. Now, I understand the compulsion to protect everyone in the name of some social good, at the very least the "not as fortune as me-group".
But why are we removing the need/worry for individuals to do this for themselves? I say this because I know for a fact that this is achievable for individuals (even poor ones). For a quite-honestly, tiny-fraction of my salary, I get all sorts of income-protection. Due to illness, terminal disease, disability, everything. Add on top of that life-insurance for my family to pay off the loan-amount on the mortgage and have them covered till my child is reasonably on his way to college, if I should leave them early.
These aren't some pipe-dream schemes or ideas, they exist. And people can get them, without the need to beg some "noble" politician to give it to them for free in return for votes/power.