My personal theory: if people even had the remotest inkling that the insurance would fail, then it is next to useless. The point of it is to prevent the majority of people from inciting a bank run since they know for sure that their money is safe. It's a bit of weird game theory.

There is no equivalent to a bank run risk on SS/Medicare so why put it in. Putting it in also means that these programs could cause massive inflation if the US Gov had to print money to finance them.