In the New York Times, Robin Roner and David E. Rosenbaum write,
The average retirement age in 1940 was 68. As recently as 1965, about two-thirds of workers did not begin drawing Social Security benefits until they were 65 or older. Now, more than half retire at 62 or younger, and three-quarters receive their first benefit checks before they are 65.
The article says that raising the retirement age is the least popular option for dealing with Social Security. This tells me that people do not view Social Security as insurance.
The insurance aspect of Social Security is that, like any annuity, it protects you against the risk of outliving your assets. If you were buying Social Security as insurance, then the premiums would be lower the later the age at which you chose to collect it. And if what people valued were the insurance aspect, then most people would prefer low premiums and benefits that kick in when they get really old. That would be better than high premiums and benefits that kick in when you are 60.
From the resistance to raising the retirement age, I conclude that what people value about Social Security has little or nothing to do with insurance or risk aversion.