This has been the dream of right wingers for decades.....
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Anti-big govt and free marketers believe that private insurance companies can do a better job than big govt SS. Big financial corps will welcome the billions that will flow right into their hands.
As it turns out, countries which followed that route found that it gave worse outcomes through higher overheads (less economies of scale) and many at the bottom half will end up with less savings at the end. The privatized system will quickly be under pressure of insolvency and probably require a bailout as per the Chilean case.