It is a good question, because inquiring about what the government policies should be, or do, directly relates to what being a citizen is supposed to be.
A government is an entity established by the same individuals making part of it, to ease decision making; and it represents the leading part of a community (and of course a state or a nation).
As far as whether providing sponsored programs (like insurance, so to speak) to the individuals within such community or not; it's absolutely up to the will of the very members of such alluded community or nation.
When it comes to democratic governments, so to speak, it entirely depends on the agreement between the people of each nation (it's members) upon establishing what is more convenient regarding the well being of the very individuals making part of it.
Thus, if the will of the people ("the will of the government") matches the well being of the members of a democratic nation, makes total sense applying policies like insurance programs and any other sponsored programs that help in contingency times, or when the unexpected happens to the very members of the nation.
