You have to watch closely as the privatizers describe their schemes. But no matter how you divvy it up, the same money can't be used twice. That is the problem with Social Security now, and it is the problem with privatization. All you've said when you endorse privatization is that if there were water, it should be used to make lemonade. Not obviously wrong, but not terribly helpful.
Privatization is a shell game in a second way.
It is supposed to bring more money into the system because returns on private securities are generally higher than returns on government bonds. Even members of the recent commission who oppose full privatization supported investing part of Social Security's accumulated surplus in the private marketplace. The net effect on national savings, and therefore on overall economic growth, is zilch. Every dollar more for Social Security is a dollar less for someone else. Also, the arrival of this huge pot of money looking for a home will depress returns in the private economy, while the need to attract an equally huge pot of money into the Treasury to replace the lost revenue will increase the returns on government bonds.