Hacker writes one of the best explanations I've seen of what insurance in general, and social insurance and particular can do (emphasis mine):
The breakthrough of 1935 was momentous all the same, for Social Security embodied a bold new imperative of government action: insurance. The word rings familiar today, but it once had a radical air. Insurance was an affirmation of free will over fate. If not an effort to stay the hand of God, it was an attempt to soften his blow…
The intelligence of insurance became genius when insurance principles were coupled with the power of the state to require participation and ensure adequate and affordable coverage. "Social Insurance," as it was called, transformed individual misfortunes into common problems. It made the inevitable dislocations of capitalist society risks that could be managed and redistributed, rather than blows of fate that could only be feared and suffered. The "insurance" in social insurance came from the power of aggregation: Risks that could devastate an individual or community could be managed if they were spread across many individuals and many communities. The "social" in social insurance came from the principles of shared fate, the reassurance that "we're all in this together." All insurance pools risks. Only social insurance pools risks on terms that enable the poor as well as the rich, aged as well as the young, the ill as well as the healthy to afford protection. The crafters of the Economic Security Act believed that insurance had to be available and within the means of those who needed insurance most.
At the heart of this belief was a simple conviction: broadly distributed threats to economic well-being - sickness, injury, disability, unemployment, penurious old age- were not the responsibility of individuals alone. They were a widespread and often unavoidable feature of an interdependent industrial society. And because they were, the cost of these risks should be distributed widely across the citizenry, not concentrated on those unlucky enough to experience them- a goal made possible by the unique power of government to compel participation and require contributions. Government could pool the risks of millions of citizens. It could guarantee that even workers of limited means were able to afford basic protection. And it could require that everyone contributed to this common pool throughout their lives, rather than waiting until they fell on hard times or disaster struck, when- for all but the richest- it would be too late.
I don't like all of the policy prescriptions, but this is a great book for understanding the underlying tensions in battles over programs like Social Security and national healthcare reform, and it offers a powerful argument about where our interests lie.