Galveston County, Texas provides a working example of a privatized Socal Security system, which they enacted just before a "reform" passed, preventing localities from opting out of the federal system. In the quoted examples of workers whose incomes ranged from $17,000/year to $75,000/year, their benefits were anywhere from 1.5x to 3x the equivalent federal Social Security check.
Gosh, it can't be taken away by government fiat, it won't result in higher taxes or inflation, and you get a bigger check. How dare anyone propose such a thing?
Another thought just occurred to me: Since, if nothing is done, the problem gets worse and worse over time, and future generations will face anything from hardship to complete disaster, why aren't any of the supporters of privatization using the obvious line, the basic, Politics 101 manipulative ploy, here in the one instance that it might actually be a legitimate argument:
We have to do this for the children!